Bell Work. Using CONDUCTION, a neutral metal sphere is touched by a negatively charged metal rod. During the process, electrons are transferred from the _____ to the _____ and the sphere acquires a _____ charge. neutral sphere, charged rod, negative neutral sphere, charged rod, positive
Bell Work Using CONDUCTION, a neutral metal sphere is touched by a negatively charged metal rod. During the process, electrons are transferred from the _____ to the _____ and the sphere acquires a _____ charge. neutral sphere, charged rod, negative neutral sphere, charged rod, positive charged rod, neutral sphere, negative charged rod, neutral sphere, positive ... nonsense! None of these describe what occurs.
Charging by Conduction
Physics Coach Stephens
Charging by Conduction Charging by conduction involves the contact of a charged object to a neutral object. Suppose that a positively charged aluminum plate is touched to a neutral metal sphere. The neutral metal sphere becomes charged as the result of being contacted by the charged aluminum plate. Or suppose that a negatively charged metal sphere is touched to the top plate of a neutral needle electroscope. The neutral electroscope becomes charged as the result of being contacted by the metal sphere. And finally, suppose that an uncharged physics student stands on an insulating platform and touches a negatively charged Van de Graaff generator. The neutral physics student becomes charged as the result of contact with the Van de Graaff generator. Each of these examples involves contact between a charged object and a neutral object. In contrast to induction, where the charged object is brought near but never contacted to the object being charged, conduction charging involves making the physical connection of the charged object to the neutral object. Because charging by conduction involves contact, it is often called charging by contact.
Charging by Conduction Using a Negatively Charged Object To explain the process of charging by contact, we will first consider the case of using a negatively charged metal sphere to charge a neutral needle electroscope. Understanding the process demands that you understand that like charges repel and have an intense desire to reduce their repulsions by spreading about as far as possible. A negatively charged metal sphere has an excess of electrons; those electrons find each other repulsive and distance themselves from each other as far as possible. The perimeter the sphere is the extreme to which they can go. If there was ever a conducting pathway to a more spacious piece of real estate, one could be sure that the electrons would be on that pathway to the greener grass beyond. In human terms, electrons living in the same home despise each other and are always seeking a home of their own or at least a home with more rooms.
Continued… Given this understanding of electron-electron repulsions, it is not difficult to predict what excess electrons on the metal sphere would be inclined to do if the sphere were touched to the neutral electroscope. Once the contact of the sphere to the electroscope is made, a countless number of excess electrons from the sphere move onto the electroscope and spread about the sphere-electroscope system. In general, the object that offers the most space in which to "hang out" will be the object that houses the greatest number of excess electrons. When the process of charging by conduction is complete, the electroscope acquires an excess negative charge due to the movement of electrons onto it from the metal sphere. The metal sphere is still charged negatively, only it has less excess negative charge than it had prior to the conduction charging process.
Charging by Conduction Using a Positively Charged Object The previous example of charging by conduction involved touching a negatively charged object to a neutral object. Upon contact, electrons moved from the negatively charged object onto the neutral object. When finished, both objects were negatively charged. But what happens if a positively charged object is touched to a neutral object? To investigate this question, we consider the case of a positively charged aluminum plate being used to charge a neutral metal sphere by the process of conduction.
Continued… The diagram below depicts the use of a positively charged aluminum plate being touched to a neutral metal sphere. A positively charged aluminum plate has an excess of protons. When looked at from an electron perspective, a positively charged aluminum plate has a shortage of electrons. In human terms, we could say that each excess proton is rather discontented. It is not satisfied until it has found a negatively charged electron with which to co-habitate. However, since a proton is tightly bound in the nucleus of an atom, it is incapable of leaving an atom in search of that longed-for electron. It can however attract a mobile electron towards itself.
Continued… And if a conducting pathway is made between a collection of electrons and an excess proton, one can be certain that there is likely an electron that would be willing to take the pathway. So when the positively charged aluminum plate is touched to the neutral metal sphere, countless electrons on the metal sphere migrate towards the aluminum plate. There is a mass migration of electrons until the positive charge on the aluminum plate-metal sphere system becomes redistributed. Having lost electrons to the positively charged aluminum plate, there is a shortage of electrons on the sphere and an overall positive charge. The aluminum plate is still charged positively; only it now has less excess positive charge than it had before the charging process began.
Why Would the Electrons Move? The above explanation might raise a rather difficult question: Why would an electron on the previously neutral metal sphere desire to move off the metal sphere in the first place? The metal sphere is neutral; every electron on it must be satisfied since there is a corresponding proton present. What would possibly induce an electron to go through the effort of migrating to a different territory in order to have what it already has?
What Can an Electron do for his Country? The best means of answering this question requires an understanding of the concept of electric potential. But since that concept does not arise until the next unit , a different approach to an answer will be taken. It ends up that electrons and protons are not as independent and individualized as we might think. From a human perspective, electrons and protons can't be thought of as independent citizens in a free enterprise system of government. Electrons and protons don't actually do what is best for themselves, but must be more social-minded. They must act like citizens of a state where the rule of law is to behave in a manner such that the overall repulsive affects within the society are reduced and the overall attractive affects are maximized. Electrons and protons will be motivated not by what is good for them, but rather by what is good for the country. And in this sense, a country's boundary extends to the perimeter of the conductor material that an excess electron is within. And in this case, an electron in the metal sphere is part of a country that extends beyond the sphere itself and includes the entire aluminum plate. So by moving from the metal sphere to the aluminum plate, an electron is able to reduce the total amount of repulsive affects within that country. It serves to spread the excess positive charge over a greater surface area, thus reducing the total amount of repulsive forces between excess protons.
Law of Conservation of Charge In each of the other methods of charging discussed - charging by friction and charging by induction - the law of conservation of charge was illustrated. The law of conservation of charge states that charge is always conserved. When all objects involved are considered prior to and after a given process, we notice that the total amount of charge among the objects is the same before the process starts as it is after the process ends. The same conservation law is observed during the charging by conduction process. If a negatively charged metal sphere is used to charge a neutral electroscope, the overall charge before the process begins is the same as the overall charge when the process ends. So if before the charging process begins, the metal sphere has 1000 units of negative charge and the electroscope is neutral, the overall charge of the two objects in the system is -1000 units. Perhaps during the charging process, 600 units of negative charge moved from the metal sphere to the electroscope. When the process is complete, the electroscope would have 600 units of negative charge and the metal sphere would have 400 units of negative charge (the original 1000 units minus the 600 units it transferred to the electroscope). The overall charge of the two objects in the system is still -1000 units. The overall charge before the process began is the same as the overall charge when the process is completed. Charge is neither created nor destroyed; it is simply transferred from one object to another object in the form of electrons.
Conduction Charging Requires a Conductor In all of these examples, the charging by conduction process involved the touching of two conductors. Does contact charging have to occur through the contact of two conductors? Can an insulator conduct a charge to another object upon touching? And can an insulator be charged by conduction? A complete discussion of these questions can get messy and quite often leads to a splitting of hairs over the definition of conduction and the distinction between conductors and insulators. The belief is taken here that only a conductor can conduct charge to another conductor. The process of noticeably charging an object by contact involves the two contacting objects momentarily sharing the net excess charge. The excess charge is simply given a larger area over which to spread in order to reduce the total amount of repulsive forces between them. This process demands that the objects be conductors in order for electrons to move about and redistribute themselves.
Continued… An insulator hinders such a movement of electrons between touching objects and about the surfaces of the objects. This is observed if an aluminum pie plate is placed upon a charged foam plate. When the neutral aluminum plate is placed upon the charged foam plate, the foam plate does not conduct its charge to the aluminum. Despite the fact that the two surfaces were in contact, charging by contact or conduction did not occur. (Or at least whatever charge transfer might have occurred was not noticeable by the customary means of using an electroscope, using a charge testing bulb or testing for its repulsion with a like-charged object.)
Insulators Charge by Lightning The charging of an electroscope by contact with a negatively charged insulating object would best be described as charging by lightning. Rather than being a process in which the two objects act together to share the excess charge, the process could best be described as the successful effort of electrons to burst through the space (air) between objects. The presence of a negatively charged plastic tube is capable of ionizing the air surrounding the tube and allowing excess electrons on the plastic tube to be conducted through the air to the electroscope.
Continued… This transfer of charge can happen with or without touching. In fact, on a dry winter day the process of charging the metal electroscope with the charged insulator often occurs while the insulator is some distance away. The dry air is more easily ionized and a greater quantity of electrons are capable of bursting through the space between the two objects. On such occasions, a crackling sound is often heard and a flash of light is seen if the room is darkened. This phenomenon, occurring from several centimeters away, certainly does not fit the description of contact charging. The two materials do not make any effort to share charge nor to act as a single object in an effort to reduce repulsive affects.
Splitting Hairs?? Is this distinction between charging by conduction and charging by lightning a splitting of hairs? Perhaps. For certain, each process involves a transfer of charge from one object to another object, yielding the same result - two like-charged objects. Yet, distinguishing between the two forms of charging is more consistent with the customary view that insulators are not conductors of charge. It also serves to explain why some insulators clearly do not always transfer their charge upon contact. This phenomenon of charging by lightning will be revisited during a discussion of electric fields and lightning discharges.
Check Your Understanding A neutral metal sphere is touched by a negatively charged metal rod. As a result, the sphere will be ____ and the metal rod will be ____. Select the two answers in their respective order. a. positively charged b. negatively charged c. neutral d. much more massive e. ... not enough information to tell
Answer #1 Answer: B & B This is a case of charging by conduction. When a charged object is used to charge a neutral object by conduction, the previously neutral object acquires the same type of charge as the charged object. The charge object maintains the same type of charge that it originally had. So in this case, both objects have a negative charge.
CYU #2 A neutral metal sphere is touched by a negatively charged metal rod. During the process, electrons are transferred from the _____ to the _____ and the sphere acquires a _____ charge. neutral sphere, charged rod, negative neutral sphere, charged rod, positive charged rod, neutral sphere, negative charged rod, neutral sphere, positive ... nonsense! None of these describe what occurs.
Answer #2 Answer: C During charging by conduction, both objects acquire the same type of charge. If a negative object is used to charge a neutral object, then both objects become charged negatively. In order for the neutral sphere to become negative, it must gain electrons from the negatively charged rod.
CYU #3 A neutral metal sphere is touched by a positively charged metal rod. During the process, protons are transferred from the _____ to the _____ and the sphere acquires a _____ charge. a. charged rod, neutral sphere, negative b. charged rod, neutral sphere, positive c. neutral sphere, charged rod, negative d. neutral sphere, charged rod, positive e. ... nonsense! None of these describe what occurs.
Answer #3 Answer: E Protons are never transferred in electrostatic activities. In this case, electrons are transferred from the neutral object to the positively charged rod and the sphere becomes charged positively.
CYU #4 A metal sphere is electrically neutral. It is touched by a positively charged metal rod. As a result, the metal sphere becomes charged positively. Which of the following occur during the process? List all that apply. a. The metal sphere gains some protons. b. Electrons are transferred from the sphere to the rod. c. The metal sphere loses electrons. d. The overall charge of the system is conserved. e. Protons are transferred from the rod to the sphere. f. Positive electrons are moved between the two objects.
Answer #4 Answer: BCD In electrostatic activities, protons are never transferred (which rules out choices a and e). Electrons are not positively charged (ruling out choice e). Choices B, C and D are all true and explain the essential nature of the conduction charging process.
Grounding – The Removal of a Charge
Physics Coach Stephens
Grounding – The Removal of a Charge The previous three sections discussed the three common methods of charging - charging by friction, charging by induction, and charging by conduction. A discussion of charging would not be complete without a discussion of uncharging. Objects with an excess of charge - either positive or negative - can have this charge removed by a process known as grounding. Grounding is the process of removing the excess charge on an object by means of the transfer of electrons between it and another object of substantial size. When a charged object is grounded, the excess charge is balanced by the transfer of electrons between the charged object and a ground. A ground is simply an object that serves as a seemingly infinite reservoir of electrons; the ground is capable of transferring electrons to or receiving electrons from a charged object in order to neutralize that object. In this last section, the process of grounding will be discussed.
Grounding of a Negatively Charged Electroscope To begin our discussion of grounding, we will consider the grounding of a negatively charged electroscope. Any negatively charged object has an excess of electrons. If it is to have its charge removed, then it will have to lose its excess electrons. Once the excess electrons are removed from the object, there will be equal numbers of protons and electrons within the object and it will have a balance of charge. To remove the excess of electrons from a negatively charged electroscope, the electroscope will have to be connected by a conducting pathway to another object that is capable of receiving those electrons. The other object is the ground. In typical electrostatic experiments and demonstrations, this is simply done by touching the electroscope with one's hand. Upon contact, the excess electrons leave the electroscope and enter the person who touches it. These excess electrons subsequently spread about the surface of the person.
Grounding This process of grounding works because excess electrons find each other repulsive. As is always the case, repulsive affects between like-charged electrons forces them to look for a means of spatially separating themselves from each other. This spatial separation is achieved by moving to a larger object that allows a greater surface area over which to spread. Because of the relative size of a person compared to a typical electroscope, the excess electrons (nearly all of them) are capable of reducing the repulsive forces by moving into the person (i.e., the ground). Like contact charging discussed earlier, grounding is simply another example of charge sharing between two objects. The extent to which an object is willing to share excess charge is proportional to its size. So an effective ground is simply an object with significant enough size to share the overwhelming majority of excess charge.
Grounding of a Positively Charged Electroscope The previous discussion describes the grounding of a negatively charged electroscope. Electrons were transferred from the electroscope to the ground. But what if the electroscope is positively charged? How does electron transfer allow an object with an excess of protons to become neutralized? To explore these questions, we will consider the grounding of a positively charged electroscope. A positively charged electroscope must gain electrons in order to acquire an equal number of protons and electrons. By gaining electrons from the ground, the electroscope will have a balance of charge and therefore be neutral. Thus, the grounding of a positively charged electroscope involves the transfer of electrons from the ground into the electroscope.
Continued… This process works because excess positive charge on the electroscope attracts electrons from the ground (in this case, a person). While this may disrupt any balance of charge present on the person, the significantly larger size of the person allows for the excess charge to distance itself further from each other. As in the case of grounding a negatively charged electroscope, the grounding of a positively charged electroscope involves charge sharing. The excess positive charge is shared between the electroscope and the ground. And once again, the extent to which an object is willing to share excess charge is proportional to its size. The person is an effective ground because it has enough size to share the overwhelming majority of excess positive charge.
The Need for a Conducting Pathway Any object can be grounded provided that the charged atoms of that object have a conducting pathway between the atoms and the ground. A common lab activity involves taping two straws to a charged aluminum plate. One straw is covered with aluminum foil and the other straw is bare plastic. When the aluminum-covered straw is touched, the aluminum plate loses its charge. It is grounded by means of the movement of electrons from the ground to the aluminum plate. When the plastic straw is touched, grounding does not occur. The plastic serves as an insulator and prevents the flow of electrons from the ground to the aluminum plate. Grounding requires a conducting pathway between the ground and the object to be grounded. Electrons will travel along that pathway.
Check Your Understanding A positively charged pop can is touched by a person standing on the ground. The pop can subsequently becomes neutral. The pop can becomes neutral during this process because ______. a. electrons pass from the pop can to the person (ground) b. electrons pass from the person (ground) to the pop can c. protons pass from the pop can to the person (ground) d. protons pass from the person (ground) to the pop can
Answer #1 Answer: B Protons do NOT move during electrostatic activities, so choices c and d can be ruled out. To ground a positively charged object, electrons must be added to it in order neutralize its excess positive charge. So electrons must move from the ground into the pop can.
CYU #2 A physics student, standing on the ground, touches an uncharged plastic baseball bat to a negatively charged electroscope. This will cause ___. a. the electroscope to be grounded as electrons flow out of the electroscope. b. the electroscope to be grounded as electrons flow into the electroscope. c. the electroscope to be grounded as protons flow out of the electroscope. d. the electroscope to be grounded as protons flow into the electroscope. e. the baseball bat to acquire an excess of protons. f. absolutely nothing (or very little) to happen since the plastic bat does not conduct.
Answer #2 Answer: F In order to ground an electroscope, electrons must have a conducting pathway between the ground and the object. In this case, a piece of plastic is part of the pathway connecting the ground (the student) and the charged object. Since plastic is an insulator, electrons are incapable of moving through the baseball bat. Grounding does not occur in this instance. Were there a conducting pathway available, choice a would be the proper choice.
CYU #3 TRUE or FALSE: An object that becomes grounded gains neutrons during the grounding process.
Answer #3 Answer: False Neutrons are positioned in the nucleus of an atom. And like protons, neutrons are never transferred in electrostatic experiments. They are bound in the nucleus and cannot escape by ordinary electrostatic methods.
Bell Work The symbol d in Coulomb's law equation represents the distance from ___. a. A to B b. A to D c. B to C d. B to D e. C to D f. A to G g. B to F h. C to E
Charge Interactions Revisited
Physics Coach Stephens
Charge Interactions are Forces It is possible that you might have watched two balloons repel each other a dozen or more times and never even thought of the balloon interaction as being a force. Or perhaps you have used a plastic golf tube or other object to raise small paper bits off the lab table and never thought of Newton's laws of motion. Perhaps even now you're thinking, "Why should I? That was the Newton's Laws unit and this is the Static Electricity unit." True. However, the physical world that we study does not separate itself into separate topics, as we teachers and students are prone to do. Physics has an amazing way of fitting together in a seamless fashion. The information that you have forgotten about from the Newton's laws unit has a mischievous way of creeping up on you in other units. That forgetfulness (or negligence or mere ignorance) will haunt you as you try to learn new physics. The more physics that you learn (as in really learn), the more that you come to recognize that the pieces of the physics puzzle fit together to form a unified picture of the world of sight, sound, touch and feel. Here we will explore how Newton's laws of motion fit together with the interaction of charged objects.
Felect Suppose that you hold a charged plastic golf tube above a handful of paper bits at rest on the table. The presence of the charged tube is likely to polarize a few bits of paper and then begin to exert an upward pull upon them. The attraction between a charged tube and a polarized (yet neutral) paper bit is an electrical force - Felect. Like all the forces that we’ve studied, the electrical force is a push or pull exerted upon an object as a result of an interaction with another object. The interaction is the result of electrical charges and thus it is called an electrical force.
Electrical Force is a Non-Contact Force Unlike many forces that we study, the electrical force is a non-contact force - it exists despite the fact that the interacting objects are not in physical contact with each other. The two objects can act over a separation distance and exert an influence upon each other. In this case, the plastic golf tube pulls upward upon the paper bit and a paper bit pulls downward upon the golf tube. The force is significantly small. If you were holding the golf tube, you would not likely sense the downward pull exerted upon it by the paper bit. On the other hand, the force is often large enough to either balance or even overwhelm the downward pull of gravity (Fgrav) upon the paper bit and cause it to be elevated or even accelerated off the table. Of course the actual result of the force upon the paper bit is related to Newton's laws and a free-body analysis. If at any moment, the electrical force were greater in magnitude than the gravitational force, the paper bit would be accelerated upward. And if at any moment, the electrical force is equal in magnitude to the gravitational force, the paper bit will be suspended (or levitated) in midair. The paper bit would be said to be at equilibrium.
Balloons at Equilibrium Now consider the case of the rubber balloons hanging by light threads from the ceiling. If each balloon is rubbed in the same manner (with animal fur), they each become positively charged and exert a repulsive affect upon each other. This charge interaction results in a force upon each balloon that is directed away from the balloon with which it interacts. Once more, we can identify this repulsive affect as an electrical force. This electrical force joins two other forces that act upon the balloon - the tension force and a force of gravity. Since the balloons are at rest, the three forces must balance each other such that the net force is zero. A more in-depth analysis of this force cancellation requires a discussion of vectors and is saved for the end of the lesson.
Coulomb’s Laws Both of these examples illustrate how the interaction between two charges results in a mutual force acting upon the charged objects. An electrical interaction is a force which, like any force, can be analyzed using a free-body diagram and Newton's laws. But what factors affect the magnitude of this force? Is there an equation that can be used to quantify it in the same manner as was done for the force of gravity (Fgrav = m•g) and the force of friction (Ffrict = mu•Fnorm)? The answer is Yes! Coulomb's law holds the key to understanding the answer to these questions. It is the topic of the next section of Lesson 3.
Physics Coach Stephens
Coulomb’s Law The interaction between charged objects is a non-contact force that acts over some distance of separation. Charge, charge and distance. Every electrical interaction involves a force that highlights the importance of these three variables. Whether it is a plastic golf tube attracting paper bits, two like-charged balloons repelling or a charged Styrofoam plate interacting with electrons in a piece of aluminum, there is always two charges and a distance between them as the three critical variables that influence the strength of the interaction. In this section of Lesson 3, we will explore the importance of these three variables.
Force as a Vector Quantity The electrical force, like all forces, is typically expressed using the unit Newton. Being a force, the strength of the electrical interaction is a vector quantity that has both magnitude and direction. The direction of the electrical force is dependent upon whether the charged objects are charged with like charge or opposite charge and upon their spatial orientation. By knowing the type of charge on the two objects, the direction of the force on either one of them can be determined with a little reasoning.
Continued… In the diagram below, objects A and B have like charge causing them to repel each other. Thus, the force on object A is directed away from B and the force on object B is directed away from A. On the other hand, objects C and D have opposite charge causing them to attract each other. Thus, the force on object C is directed toward object D and the force on object D is directed toward object C. When it comes to the electrical force vector, perhaps the best way to determine the direction of it is to apply the fundamental rules of charge interaction (opposites attract and likes repel) using a little reasoning.
Magnitude or Strength Electrical force also has a magnitude or strength. Like most types of forces, there are a variety of factors that influence the magnitude of the electrical force. Two like-charged balloons will repel each other and the strength of their repulsive force can be altered by changing three variables. First, the quantity of charge on one of the balloons will affect the strength of the repulsive force. The more charged a balloon is, the greater the repulsive force. Second, the quantity of charge on the second balloon will affect the strength of the repulsive force. Gently rub two balloons with animal fur and they repel a little. Rub the two balloons vigorously to impart more charge to both of them, and they repel a lot. Finally, the distance between the two balloons will have a significant and noticeable effect upon the repulsive force. The electrical force is strongest when the balloons are closest together. Decreasing the separation distance increases the force. The magnitude of the force and the distance between the two balloons is said to be inversely related.
Coulomb’s Law Equation The quantitative expression for the effect of these three variables on electric force is known as Coulomb's law. Coulomb's law states that the electrical force between two charged objects is directly proportional to the product of the quantity of charge on the objects and inversely proportional to the square of the separation distance between the two objects. In equation form, Coulomb's law can be stated as:
Continued... where Q1 represents the quantity of charge on object 1 (in Coulombs), Q2 represents the quantity of charge on object 2 (in Coulombs), and d represents the distance of separation between the two objects (in meters). The symbol k is a proportionality constant known as the Coulomb's law constant. The value of this constant is dependent upon the medium that the charged objects are immersed in. In the case of air, the value is approximately 9.0 x 109 N • m2 / C2. If the charged objects are present in water, the value of k can be reduced by as much as a factor of 80. It is worthwhile to point out that the units on k are such that when substituted into the equation the units on charge (Coulombs) and the units on distance (meters) will be canceled, leaving a Newton as the unit of force.
Continued… The Coulomb's law equation provides an accurate description of the force between two objects whenever the objects act as point charges. A charged conducting sphere interacts with other charged objects as though all of its charge were located at its center. While the charge is uniformly spread across the surface of the sphere, the center of charge can be considered to be the center of the sphere. The sphere acts as a point charge with its excess charge located at its center. Since Coulomb's law applies to point charges, the distance d in the equation is the distance between the centers of charge for both objects (not the distance between their nearest surfaces).
Continued… The symbols Q1 and Q2 in the Coulomb's law equation represent the quantities of charge on the two interacting objects. Since an object can be charged positively or negatively, these quantities are often expressed as "+" or "-" values. The sign on the charge is simply representative of whether the object has an excess of electrons (a negatively charged object) or a shortage of electrons (a positively charged object). It might be tempting to utilize the "+" and "-" signs in the calculations of force. While the practice is not recommended, there is certainly no harm in doing so. When using the "+" and "-" signs in the calculation of force, the result will be that a "-" value for force is a sign of an attractive force and a "+" value for force signifies a repulsive force. Mathematically, the force value would be found to be positive when Q1 and Q2 are of like charge - either both "+" or both "-". And the force value would be found to be negative when Q1 and Q2 are of opposite charge - one is "+" and the other is "-". This is consistent with the concept that oppositely charged objects have an attractive interaction and like charged objects have a repulsive interaction. In the end, if you're thinking conceptually (and not merely mathematically), you would be very able to determine the nature of the force - attractive or repulsive - without the use of "+" and "-" signs in the equation.
Calculations Using Coulomb’s Law In physics courses, Coulomb's law is often used as a type of algebraic recipe to solve physics word problems. Three such examples are shown here. Example A Suppose that two point charges, each with a charge of +1.00 Coulomb are separated by a distance of 1.00 meter. Determine the magnitude of the electrical force of repulsion between them. This is not the most difficult mathematical problem that could be selected. It certainly was not chosen for its mathematical rigor. The problem-solving strategy utilized here may seem unnecessary given the simplicity of the given values. Nonetheless, the strategy will be used to illustrate its usefulness to any Coulomb's law problem.
Continued… The first step of the strategy is the identification and listing of known information in variable form. Here we know the charges of the two objects (Q1 and Q2) and the separation distance between them (d). The next step of the strategy involves the listing of the unknown (or desired) information in variable form. In this case, the problem requests information about the force. So Felect is the unknown quantity. The results of the first two steps are shown below. Given: Q1 = 1.00 C Q2 = 1.00 C d = 1.00 m Find: Felect = ???
Continued… The next and final step of the strategy involves substituting known values into the Coulomb's law equation and using proper algebraic steps to solve for the unknown information. This step is shown below. Felect = k • Q1 • Q2 / d2 Felect = (9.0 x 109 N•m2/C2) • (1.00 C) • (1.00 C) / (1.00 m)2 Felect = 9.0 x 109 N The force of repulsion of two +1.00 Coulomb charges held 1.00 meter apart is 9 billion Newton. This is an incredibly large force that compares in magnitude to the weight of more than 2000 jetliners.
Micro & Nano This problem was chosen primarily for its conceptual message. Objects simply do not acquire charges on the order of 1.00 Coulomb. In fact, more likely Q values are on the order of 10-9 or possibly 10-6 Coulombs. For this reason, a Greek prefix is often used in front of the Coulomb as a unit of charge. Charge is often expressed in units of microCoulomb (µC) and nanoCoulomb (nC). If a problem states the charge in these units, it is advisable to first convert to Coulombs prior to substitution into the Coulomb's law equation. The following unit equivalencies will assist in such conversions. 1 Coulomb = 10-6microCoulomb 1 Coulomb = 10-9nanoCoulomb
Problem-Solving Strategy The problem-solving strategy used in Example A included three steps: Identify and list known information in variable form. List the unknown (or desired) information in variable form. Substitute known values into the Coulomb's law equation and using proper algebraic steps to solve for the unknown information. (In some cases and for some students, it might be easier to first do the algebra using the variables and then perform the substitution as the last step.)
Example B Two balloons are charged with an identical quantity and type of charge: -6.25 nC. They are held apart at a separation distance of 61.7 cm. Determine the magnitude of the electrical force of repulsion between them. The problem states the value of Q1 and Q2. Since these values are expressed in units of nanoCoulombs (nC), the conversion to Coulombs must be made. The problem also states the separation distance (d). Since distance is given in units of centimeters (cm), the conversion to meters must also be made. These conversions are required since the units of charge and distance in the Coulomb's constant are Coulombs and meters. The unknown quantity is the electrical force (F). The results of the first two steps are shown below. Given: Q1 = -6.25 nC = -6.25 x 10-9 C Q2 = -6.25 nC = -6.25 x 10-9 C d = 61.7 cm = 0.617 m Find: Felect = ???
Continued… The final step of the strategy involves substituting known values into the Coulomb's law equation and using proper algebraic steps to solve for the unknown information. This substitution and algebra is shown below. Felect = k • Q1 • Q2 / d2 Felect = (9.0 x 109 N•m2/C2) • (6.25 x 10-9 C) • (6.25 x 10-9 C) / (0.617 m)2 Felect = 9.23 x 10-7 N Note that the "-" sign was dropped from the Q1 and Q2 values prior to substitution into the Coulomb's law equation. As mentioned above, the use of "+" and "-" signs in the equation would result in a positive force value if Q1 and Q2 are like charged and a negative force value if Q1 and Q2 are oppositely charged. The resulting "+" and "-" signs on F signifies whether the force is attractive (a "-" F value) or repulsive (a "+" F value).
Example C Two balloons with charges of +3.37 µC and -8.21 µC attract each other with a force of 0.0626 Newton. Determine the separation distance between the two balloons. The problem states the value of Q1 and Q2. Since these values are in units of microCoulombs (µC), the conversion to Coulombs will be made. The problem also states the electrical force (F). The unknown quantity is the separation distance (d). The results of the first two steps are shown in the table below. Given: Q1 = +3.37 µC = +3.37 x 10-6 C Q2 = -8.21 µC = -8.21 x 10-6 C Felect = -0.0626 N (use a - force value since it is attractive) Find: d = ???
Continued… As mentioned above, the use of the "+" and "-" signs is optional. However, if they are used, then they have to be used consistently for the Q values and the F values. Their use in the equation is illustrated in this problem. The final step of the strategy involves substituting known values into the Coulomb's law equation and using proper algebraic steps to solve for the unknown information. In this case, the algebra is done first and the substitution is performed last. This algebra and substitution is shown below. Felect = k • Q1 • Q2 / d2 d2 • Felect = k • Q1 • Q2 d2 = k • Q1 • Q2 / Felect d = SQRT(k • Q1 • Q2) / Felect d = SQRT [(9.0 x 109 N•m2/C2) • (-8.21 x 10-6 C) • (+3.37 x 10-6 C) / (-0.0626 N)] d = Sqrt [ +3.98 m2 ] d = +1.99 m
Comparing Electrical & Gravitational Forces Electrical force and gravitational force are the two non-contact forces discussed in The Physics Classroom tutorial. Coulomb's law equation for electrical force bears a strong resemblance to Newton's equation for universal gravitation.
Continued… The two equations have a very similar form. Both equations show an inverse square relationship between force and separation distance. And both equations show that the force is proportional to the product of the quantity that causes the force - charge in the case of electrical force and mass in the case of gravitational force. Yet there are some striking differences between these two forces. First, a comparison of the proportionality constants - k versus G - reveals that the Coulomb's law constant (k) is significantly greater than Newton's universal gravitation constant (G). Subsequently a unit of charge will attract a unit of charge with significantly more force than a unit of mass will attract a unit of mass. Second, gravitational forces are only attractive; electrical forces can be either attractive or repulsive. The inverse square relationship between force and distance that is woven into the equation is common to both non-contact forces. This relationship highlights the importance of separation distance when it comes to the electrical force between charged objects. It is the focus of the next section.
Check Your Understanding The Q in Coulomb's law equation stands for the _____. a. mass of a charged object b. # of excess electrons on the object c. the current of a charged object d. the distance between charged objects e. charge of a charged object
Answer #1 Answer: E In the equation Felect = k • Q1 • Q2 / d2 , the symbol Felectrepresents the electrostatic force of attraction or repulsion between objects 1 and 2. The symbol k is Coulomb's law constant (9 x 109 N • m2 / C2), Q1 and Q2 represent the quantity of charge on object 1 and object 2, and d represents the separation distance between the objects' centers.
CYU #2 The symbol d in Coulomb's law equation represents the distance from ___. a. A to B b. A to D c. B to C d. B to D e. C to D f. A to G g. B to F h. C to E
CYU #2 The symbol d in Coulomb's law equation represents the distance from ___. a. A to B b. A to D c. B to C d. B to D e. C to D f. A to G g. B to F h. C to E
Answer #2 Answer: G In the equation Felect = k • Q1 • Q2 / d2 , the symbol Felectrepresents the electrostatic force of attraction or repulsion between objects 1 and 2. The symbol k is Coulomb's law constant (9 x 109 N • m2/ C2), Q1 and Q2 represent the quantity of charge on object 1 and object 2, and d represents the separation distance between the objects' centers.
CYU #3 Determine the electrical force of attraction between two balloons with separate charges of +3.5 x 10-8 C and -2.9 x 10-8 C when separated a distance of 0.65 m.
Answer #3 Answer: -2.16 x 10-5 N, attractive Step 1: Identify known values in variable form. Q1 = +3.5 x 10-8 C Q2 = -2.9 x 10-8 C d = 0.65 m Step 2: Identify the requested value F = ??? Step 3: Substitute and solve
CYU #4 Determine the electrical force of attraction between two balloons that are charged with the opposite type of charge but the same quantity of charge. The charge on the balloons is 6.0 x 10-7 C and they are separated by a distance of 0.50 m.
Answer #4 Answer: -0.0130 N Step 1: Identify known values in variable form. Q1 = -6.0 x 10-7 C Q2 = +6.0 x 10-7 C d = 0.50 m. Step 2: Identify requested information F = ??? Step 3: Substitute and solve.
CYU #5 Joann has rubbed a balloon with wool to give it a charge of -1.0 x 10-6 C. She then acquires a plastic golf tube with a charge of +4.0 x 10-6 C localized at a given position. She holds the location of charge on the plastic golf tube a distance of 50.0 cm above the balloon. Determine the electrical force of attraction between the golf tube and the balloon.
Answer #5 Answer: -0.144 N Step 1: Identify known values in variable form. Q1 = -1.0 x 10^-6 C Q2 = +4.0 x 10-6 C d = 50.0 cm = 0.50 m. Step 2: Identify requested information F = ??? Step 3: Substitute and solve.
CYU #6 A balloon with a charge of 4.0 µC is held a distance of 0.70 m from a second balloon having the same charge. Calculate the magnitude of the repulsive force.
Answer #6 Answer: 0.29 N Step 1: Identify known values in variable form. Q1 = -4.0 x 10^-6 C Q2 = +4.0 x 10-6 C d = 0.70 m. Step 2: Identify requested information F = ??? Step 3: Substitute and solve.
CYU #7 At what distance of separation must two 1.00-microCoulomb charges be positioned in order for the repulsive force between them to be equivalent to the weight (on Earth) of a 1.00-kg mass?
Answer #7 Answer: 0.030 m or 3.0 cm Step 1: Identify known values in variable form. Q1 = 1.0 x 10-6 C Q2 = 1.0 x 10-6 C Felect = Fgrav = mg = 1.0 • 9.8 m/s/s = 9.8 N Step 2: Identify requested information d = ??? Step 3: Substitute and solve.
Bell Work Alteration of the distance between two charged objects: Two charged objects have a repulsive force of 0.080 N. If the distance separating the objects is doubled, then what is the new force?
Inverse Square Law
Physics Coach Stephens
Inverse Square Law Science in general and Physics in particular are concerned with relationships. Cause and effect is the focus of science. Nature is probed in order to find relationships and mathematical patterns. Scientists modify a set of conditions to see if there is a pattern of behavior in another set of measurable quantities. The goal is to answer the question of how does a change in a set of variables or conditions causally effect an observable outcome? In Physics, this search for cause and effect leads to questions like: How does a force affect the acceleration of an object? How does the mass of an object affect its acceleration? How does the speed of a falling object affect the amount of air resistance that it experiences? How does the distance from a page to a light bulb affect the amount of light that illuminates the paper's surface? How does the frequency of a sound wave affect the speed at which the sound wave moves? How does the distance between two charged objects affect the force of attraction or repulsion that they encounter?
Direct & Inverse Relationships This search for cause and effect often leads to conclusive evidence that two variables are causally related (or not causally related). Careful observation and measurement might indicate that a pattern exists in which an increase in one variable always causes another measurable quantity to increase. This type of cause-effect relationship is described as being a direct relationship. Observation might also indicate that an increase in one variable always causes another measurable quantity to decrease. This type of cause-effect relationship is described as being an inverse relationship.
Inverse Relationships Inverse relationships are common in nature. In electrostatics, the electrical force between two charged objects is inversely related to the distance of separation between the two objects. Increasing the separation distance between objects decreases the force of attraction or repulsion between the objects. And decreasing the separation distance between objects increases the force of attraction or repulsion between the objects. Electrical forces are extremely sensitive to distance. These observations are commonly made during demonstrations and lab experiments. Consider a charged plastic golf tube being brought near a collection of paper bits at rest upon a table. The electrical interaction is so small at large distances that the golf tube does not seem to exert an influence upon the paper bits. Yet if the tube is brought closer, an attractive interaction is observed and the strength is so significant that the paper bits are lifted off the table. In a similar manner, charged balloons are observed to exert their greatest influence upon other charged objects when the separation distance is reduced. Electrostatic force and distance are inversely related.
Inverse Square Relationship The pattern between electrostatic force and distance can be further characterized as an inverse square relationship. Careful observations show that the electrostatic force between two point chargesvaries inversely with the square of the distance of separation between the two charges. That is, the factor by which the electrostatic force is changed is the inverse of the square of the factor by which the separation distance is changed. So if the separation distance is doubled (increased by a factor of 2), then the electrostatic force is decreased by a factor of four (2 raised to the second power). And if the separation distance is tripled (increased by a factor of 3), then the electrostatic force is decreased by a factor of nine (3 raised to the second power). This square effect makes distance of double importance in its impact upon electrostatic force.
Continued… The inverse square relationship between electrostatic force and separation distance is illustrated in the table below.
Patterns The above values illustrate a pattern: as the separation distance is doubled, the electrostatic force is decreased by a factor of four. For instance, the distance in Row 2 is twice the distance of Row 1; and the electrostatic force in Row 2 is one-fourth the electrostatic force of Row 1. A comparison of Row 1 and Row 3 illustrate that as the distance is increased by a factor three, the force is decreased by a factor of nine. The distance in Row 3 is three times that of Row 1 and the force in Row 3 is one-ninth that of Row 1. A similar comparison of Rows 1 and Row 4 illustrates that as the distance is increased by a factor of four, the electrostatic force is decreased by a factor of 16. The distance in Row 4 is four times that of Row 1 and the force in Row 4 is one-sixteenth that of Row 1.
Continued… The equation shows that the distance squared term is in the denominator of the equation, opposite the force. This illustrates that force is inversely proportional to the square of the distance.
Check Your Understanding Alteration in the quantity of charge: Two charged objects have a repulsive force of 0.080 N. If the charge of one of the objects is doubled, then what is the new force?
Answer #1 Answer: 0.160 N Explanation: Electrostatic force is directly related to the charge of each object. So if the charge of one object is doubled, then the force will become two times greater. Two times 0.080 N is 0.160 N.
CYU #2 Alteration of the distance between two charged objects: Two charged objects have a repulsive force of 0.080 N. If the distance separating the objects is doubled, then what is the new force?
Answer #2 Answer: 0.020 N Explanation: The electrostatic force is inversely related to the square of the separation distance. So if d is two times larger, then F is four times smaller - that is, one-fourth the original value. One-fourth of 0.080 N is 0.020 N.
CYU #3 Alteration in both the quantity of charge and the distance: Two charged objects have a repulsive force of 0.080 N. If the charge of one of the objects is doubled, and the distance separating the objects is doubled, then what is the new force?
Answer #3 Answer: 0.040 N Explanation: The electrostatic force is directly related to the product of the charges and inversely related to the square of the separation distance. Doubling one of the charges would serve to double the force. Doubling the distance would serve to reduce the force by a factor of four. The combined affect of these two variations would be to decrease the force by a factor of two - changing it from 0.080 N to 0.040 N.
Bell Work It is observed that Balloon A is charged negatively. Balloon B exerts a repulsive affect upon balloon A. Would the electric field vector created by balloon B be directed towards B or away from B? __________Explain your reasoning.
Answer Bell Work Answer: Towards B If balloon B repels balloon A then balloon B must be negatively charged. The electric field vectors are always directed towards negatively charged objects. As such, the E vectors must be towards balloon B.
Physics Coach Stephens
Action-at-a-Distance The underlying and primary question being addressed in this unit is: How can an object be charged and what affect does that charge have upon other objects in its vicinity? Early in Lesson 1, we investigated charge interactions - the affect of a charged object upon other objects of the same type of charge, of an opposite type of charge and of no charge whatsoever. In Lesson 3, the concept of the interaction between charges was revisited and Coulomb's law was introduced to express charge interactions in quantitative terms. Electric force was described as a non-contact force. A charged balloon can have an attractive affect upon an oppositely charged balloon even when they are not in contact. The electric force acts over the distance separating the two objects. Electric force is an action-at-a-distance force. In Lesson 4 of this unit, we will explore this concept of action-at-a-distance using a different concept known as the electric field. As is the usual case, we will begin conceptually and then enter into mathematical expressions that express the concept of an electric field in mathematical terms.
Contact & Non-Contact Forces At the time that the concept of force was introduced, it was mentioned that there are two categories of forces - contact forces and non-contact forces. Electrical force and gravitational force were both listed as non-contact forces. The gravitational forceis a force that most of us are familiar with. Gravitational forces are action-at-a-distance forces that act between two objects even when they are held some distance apart. If you watch a roller coaster car move along its course, then you are witnessing an action-at-a-distance. The Earth and the coaster car attract even though there is no physical contact between the two objects. If you watch a baseball travel its parabolic trajectory at a baseball park, then you are witnessing an action-at-a-distance. The Earth and the baseball attract even though there is no physical contact between the two objects. In each of these examples, the mass of the Earth exerted an influence over a distance, affecting other objects of mass that were in the surrounding neighborhood.
Observed Non-Contact Forces The action-at-a-distance nature of the electrical force is commonly observed numerous times during lab activities and demonstrations in a Physics classroom. A charged plastic golf tube might be held above bits of paper on a lab bench. The plastic tube attracts the paper bits even though physical contact is not made with the paper bits. The charged plastic tube might also be held near a charged rubber balloon; and even without physical contact, the tube and the balloon act over a distance. The charged plastic tube exerts its influence over a distance, affecting other charged objects that were in the surrounding neighborhood. Consider a charged foam plate held above an aluminum pie plate without touching it. The charged foam plate exerts an influence upon charged electrons in the aluminum plate even though physical contact is not made. The charged foam plate exerts its influence over a distance, affecting other charged objects in the surrounding neighborhood. Consider a physics demonstration in which a charged object is brought near the plate of a needle electroscope. Prior to any contact between the electroscope plate and the charged object, the needle of the electroscope begins to deflect. The charged object exerts an influence upon charged electrons in the electroscope even though physical contact is not made. The charged object affects other charged objects that were in the surrounding neighborhood.
The Electric Field Concept As children grow, they become very accustomed to contact forces; but an action-at-a-distance force upon first observation is quite surprising. Seeing two charged balloons repel from a distance or two magnets attract from a distance raises the eyebrow of a child and maybe even causes a chuckle or a "wow." Indeed, an action-at-a-distance or non-contact force is quite unusual. Football players don't run down the field and encounter collision forces from five yards apart. The rear-end collision at a stop sign is not characterized by repulsive forces that act upon the colliding cars at a spatial separation of 10 meters. And (with the exception modern WWF wrestling matches) the fist of one fighter does not act from 12 inches away to cause the forehead of a second fighter to be knocked backwards. Contact forces are quite usual and customary to us. Explaining a contact force that we all feel and experience on a daily basis is not difficult. Non-contact forces require a more difficult explanation. After all, how can one balloon reach across space and pull a second balloon towards it or push it away? The best explanation to this question involves the introduction of the concept of electric field.
Field Forces Action-at-a-distance forces are sometimes referred to as field forces. The concept of a field force is utilized by scientists to explain this rather unusual force phenomenon that occurs in the absence of physical contact. While all masses attract when held some distance apart, charges can either repel or attract when held some distance apart. An alternative to describing this action-at-a-distance affect is to simply suggest that there is something rather strange about the space surrounding a charged object. Any other charged object that is in that space feels the affect of the charge. A charged object creates an electric field - an alteration of the space in the region that surrounds it. Other charges in that field would feel the unusual alteration of the space. Whether a charged object enters that space or not, the electric field exists. Space is altered by the presence of a charged object. Other objects in that space experience the strange and mysterious qualities of the space.
Van De Graaff Generator The strangeness of the space surrounding a charged object is often experienced first hand by the use of a Van de Graaff generator. A Van de Graaff generator is a large conducting sphere that acquires a charge as electrons are scuffed off of a rotating belt as it moves past sharp elongated prongs inside the sphere. The buildup of static charge on the Van de Graaff generator is much greater than that on a balloon rubbed with animal fur or an aluminum plate charged by induction. On a dry day, the buildup of charge becomes so great that it can exert influences on charged balloons held some distance away. If you were to walk near a Van de Graaff generator and hold out your hand, you might even notice the hairs on your hand standing up. And if you were to slowly walk near a Van de Graaff generator, your eyebrows might begin to feel quite staticy. The Van de Graaff generator, like any charged object, alters the space surrounding it. Other charged objects entering the space feel the strangeness of that space. Electric forces are exerted upon those charged objects when they enter that space. The Van de Graaff generator is said to create an electric field in the space surrounding it.
Quantifying an Electric Field Now all of a sudden, the discussion of electric field begins to take on a quantitative nature. Some electric fields are stronger or more intense than others. And perhaps the strength of the electric field could be measured and quantified. And clearly charge and distance seem to be two variables that affect the strength of an electric field. In the next section of Lesson 4, the quantitative nature of electric field will be discussed. The question of "How can the strength of an electric field be quantified?" will be explored. We will move beyond the mere concept of the electric field to the mathematics of the electric field.
Electric Field Intensity
Review In the previous section of Lesson 4, the concept of an electric field was introduced. It was stated that the electric field concept arose in an effort to explain action-at-a-distance forces. All charged objects create an electric field that extends outward into the space that surrounds it. The charge alters that space, causing any other charged object that enters the space to be affected by this field. The strength of the electric field is dependent upon how charged the object creating the field is and upon the distance of separation from the charged object. In this section of Lesson 4, we will investigate electric field from a numerical viewpoint - the electric field strength.
The Force Per Charge Ratio Electric field strength is a vector quantity; it has both magnitude and direction. The magnitude of the electric field strength is defined in terms of how it is measured. Let's suppose that an electric charge can be denoted by the symbol Q. This electric charge creates an electric field; since Q is the source of the electric field, we will refer to it as the source charge. The strength of the source charge's electric field could be measured by any other charge placed somewhere in its surroundings. The charge that is used to measure the electric field strength is referred to as a test charge since it is used to test the field strength. The test charge has a quantity of charge denoted by the symbol q. When placed within the electric field, the test charge will experience an electric force - either attractive or repulsive. As is usually the case, this force will be denoted by the symbol F. The magnitude of the electric field is simply defined as the force per charge on the test charge.
Electric Field Strength Equation If the electric field strength is denoted by the symbol E, then the equation can be rewritten in symbolic form as: The standard metric units on electric field strength arise from its definition. Since electric field is defined as a force per charge, its units would be force units divided by charge units. In this case, the standard metric units are Newton/Coulomb or N/C.
Test Charge In the above discussion, you will note that two charges are mentioned - the source charge and the test charge. Two charges would always be necessary to encounter a force. In the electric world, it takes two to attract or repel. The equation for electric field strength (E) has one of the two charge quantities listed in it. Since there are two charges involved, a student will have to be ultimately careful to use the correct charge quantity when computing the electric field strength. The symbol q in the equation is the quantity of charge on the test charge (not the source charge). Recall that the electric field strength is defined in terms of how it is measured or tested; thus, the test charge finds its way into the equation. Electric field is the force per quantity of charge on the test charge.
Another Electric Field Strength Formula The above discussion pertained to defining electric field strength in terms of how it is measured. Now we will investigate a new equation that defines electric field strength in terms of the variables that affect the electric field strength. To do so, we will have to revisit the Coulomb's law equation. Coulomb's law states that the electric force between two charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between their centers. When applied to our two charges - the source charge (Q) and the test charge (q) - the formula for electric force can be written as: If the expression for electric force as given by Coulomb's law is substituted for force in the above E =F/q equation, a new equation can be derived as shown below. Note that the derivation above shows that the test charge q was canceled from both numerator and denominator of the equation. The new formula for electric field strength (shown inside the box) expresses the field strength in terms of the two variables that affect it. The electric field strength is dependent upon the quantity of charge on the source charge (Q) and the distance of separation (d) from the source charge.
An Inverse Square Law Like all formulas in physics, the formulas for electric field strength can be used to algebraically solve physics word problems. And like all formulas, these electric field strength formulas can also be used to guide our thinking about how an alteration of one variable might (or might not) affect another variable. One feature of this electric field strength formula is that it illustrates an inverse square relationship between electric field strength and distance. The strength of an electric field as created by source charge Q is inversely related to square of the distance from the source. This is known as an inverse square law. Electric field strength is location-dependent, and its magnitude decreases as the distance from a location to the source increases. And by whatever factor the distance is changed, the electric field strength will change inversely by the square of that factor. So if separation distance increases by a factor of 2, the electric field strength decreases by a factor of 4 (2^2). If the separation distance increases by a factor of 3, the electric field strength decreases by a factor of 9 (3^2). And finally, if separation distance decreases by a factor of 2, the electric field strength increases by a factor of 4 (2^2).
The Direction of the Electric Field Vector As mentioned earlier, electric field strength is a vector quantity. Unlike a scalar quantity, a vector quantity is not fully described unless there is a direction associated with it. The magnitude of the electric field vector is calculated as the force per charge on any given test charge located within the electric field. The force on the test charge could be directed either towards the source charge or directly away from it. The precise direction of the force is dependent upon whether the test charge and the source charge have the same type of charge or the opposite type of charge. To resolve the dilemma of whether the electric field vector is directed towards or away from the source charge, a convention has been established. The worldwide convention that is used by scientists is to define the direction of the electric field vector as the direction that a positive test charge is pushed or pulled when in the presence of the electric field. By using the convention of a positive test charge, everyone can agree upon the direction of E.
Continued… Given this convention of a positive test charge, several generalities can be made about the direction of the electric field vector. A positive source charge would create an electric field that would exert a repulsive affect upon a positive test charge. Thus, the electric field vector would always be directed away from positively charged objects. On the other hand, a positive test charge would be attracted to a negative source charge. Therefore, electric field vectors are always directed towards negatively charged objects.
Check Your Understanding Charge Q acts as a point charge to create an electric field. Its strength, measured a distance of 30 cm away, is 40 N/C. What is the magnitude of the electric field strength that you would expect to be measured at a distance of ... a. 60 cm away? b. 15 cm away? c. 90 cm away? d. 3 cm away? e. 45 cm away?
Answer #1 The electric field strength is inversely related to the square of the distance. So by whatever factor d changes by, the E value is altered in the inverse direction by the square of that factor. The specifics are as follows: a) d increases by a factor of 2; divide the original E by 4. b) d decreases by a factor of 2; multiply the original E by 4. c) d increases by a factor of 3; divide the original E by 9. d) d decreases by a factor of 10; multiply the original E by 100. e) d increases by a factor of 1.5; divide the original E by (1.5)2.
CYU #2 Use your understanding of electric field strength to complete the following table.
Answer #2 a) Find E by calculating F / q (both of which are given). b) Find F by multiplying E by q (both of which are given). c) Find E by calculating F/q (both of which are given). d) Find F by multiplying E by q (both of which are given). e) First find E, reasoning that since Q and d are the same in this row as the previous row, the E value must also be the same. Then find q by multiplying the given value of F by your calculated value for E. f) Find F by multiplying E by q (both of which are given). g) First find E, reasoning that since Q and d are the same in this row as the previous row, the E value must also be the same. Then find F by multiplying the calculated value of E by the given value of q. h) First find E, reasoning that since Q and d are the same in this row as the previous row, the E value must also be the same. Then find q by multiplying the given value of F by your calculated value for E. i) Any value of q and F can be selected provided that the F/q ratio is equal to the given value of E. j) First find E, reasoning that since Q and d are the same in this row as the previous row, the E value must also be the same. Then any value of q and F can be selected provided that the F/q ratio is equal to the determined value of E.
CYU #4 A negative source charge (Q) is shown in the diagram below. This source charge can create an electric field. Various locations within the field are labeled. For each location, draw an electric field vector in the appropriate direction with the appropriate relative magnitude. That is, draw the length of the E vector long wherever the magnitude is large and short wherever the magnitude is small.
Answer #4 An electric field vector at any given location points in the direction which a positive test charge would be pushed or pulled if placed at that location. The electric field vector in each case should be directed towards the center of the source charge since a positive test charge would be attracted to this negative source charge. The length of the vector should be inversely related to the distance from the center of the source charge. Thus, locations B and C would have the longest arrow. Location D appears next closest and should have the next longest arrow. And of course F and then E would have the shortest vector arrows since they are furthest from the source charge.
Bell Work Several electric field line patterns are shown in the diagrams below. Which of these patterns are incorrect? _________ Explain what is wrong with all incorrect diagrams.
Bell Work Answer Answer: C, D and E In C, the lines are directed towards a positively charged object. In D, the lines are not symmetrically positioned despite the fact that the object is a symmetrical sphere. In E, the lines are directed away from a negative charge.
Electric Field Lines
Physics Coach Stephens
Review In the previous section, the vector nature of the electric field strength was discussed. The magnitude or strength of an electric field is related directly to the quantity of charge on the source charge and inversely to the distance from the source charge. The direction of the electric field is always directed in the direction that a positive test charge would be pushed or pulled if placed in the space surrounding the source charge. Since electric field is a vector quantity, it can be represented by a vector arrow. For any given location, the arrows point in the direction of the electric field and their length is proportional to the strength of the electric field at that location. Such vector arrows are shown in the diagram below. Note that the lengths of the arrows are longer when closer to the source charge and shorter when further from the source charge.
Electric Field Lines of Force A more useful means of visually representing the vector nature of an electric field is through the use of electric field lines of force. Rather than draw countless vector arrows in the space surrounding a source charge, it is perhaps more useful to draw a pattern of several lines that extend between infinity and the source charge. These pattern of lines, sometimes referred to as electric field lines, point in the direction that a positive test charge would accelerate if placed upon the line. As such, the lines are directed away from positively charged source charges and toward negatively charged source charges. To communicate information about the direction of the field, each line must include an arrowhead that points in the appropriate direction. An electric field line pattern could include an infinite number of lines. Because drawing such large quantities of lines tends to decrease the readability of the patterns, the number of lines is usually limited. The presence of a few lines around a charge is typically sufficient to convey the nature of the electric field in the space surrounding the lines.
Rules for Drawing Electric Field Patterns There are a variety of conventions and rules to drawing such patterns of electric field lines. The conventions are simply established in order that electric field line patterns communicate the greatest amount of information about the nature of the electric field surrounding a charged object. One common convention is to surround more charged objects by more lines. Objects with greater charge create stronger electric fields. By surrounding a highly charged object with more lines, one can communicate the strength of an electric field in the space surrounding a charged object by the line density.
Density of Lines Not only does the density of lines surrounding any given object reveal information about the quantity of charge on the source charge, the density of lines at a specific location in space reveals information about the strength of the field at that location. Consider the object shown below: Two different circular cross-sections are drawn at different distances from the source charge. These cross-sections represent regions of space closer to and further from the source charge. The field lines are closer together in the regions of space closest to the charge; and they are spread further apart in the regions of space furthest from the charge. Based on the convention concerning line density, one would reason that the electric field is greatest at locations closest to the surface of the charge and least at locations further from the surface of the charge. Line density in an electric field line pattern reveals information about the strength or magnitude of an electric field.
A Second Rule A second rule for drawing electric field lines involves drawing the lines of force perpendicular to the surfaces of objects at the locations where the lines connect to object's surfaces. At the surface of both symmetrically shaped and irregularly shaped objects, there is never a component of electric force that is directed parallel to the surface. The electric force, and thus the electric field, is always directed perpendicular to the surface of an object. If there were ever any force parallel to the surface, then any excess charge on the surface of a source charge would begin to accelerate. This would lead to the occurrence of an electric current within the object; this is never observed in static electricity. Once a line of force leaves the surface of an object, it will often alter its direction. This occurs when drawing electric field lines for configurations of two or more charges as discussed in the section below.
Final Rule A final rule for drawing electric field lines involves the intersection of lines. Electric field lines should never cross. This is particularly important (and tempting to break) when drawing electric field lines for situations involving a configuration of charges (as in the section below). Electric field lines reveal information about the direction (and the strength) of an electric field within a region of space. If the lines cross each other at a given location, then there must be two distinctly different values of electric field with their own individual direction at that given location. This could never be the case. Every single location in space has its own electric field strength and direction associated with it. Consequently, the lines representing the field cannot cross each other at any given location in space.
Electric Field Lines for Configurations of Two or More Charges In the examples above, we've seen electric field lines for the space surrounding single point charges. But what if a region of space contains more than one point charge? How can the electric field in the space surrounding a configuration of two or more charges be described by electric field lines? To answer this question, we will first return to our original method of drawing electric field vectors. Suppose that there are two positive charges - charge A (QA) and charge B (QB) - in a given region of space. Each charge creates its own electric field. At any given location surrounding the charges, the strength of the electric field can be calculated using the expression kQ/d2. Since there are two charges, the kQ/d2 calculation would have to be performed twice at each location - once with kQA/dA2 and once with kQB/dB2 (dA is the distance from that location to the center of charge A and dB is the distance from that location to the center of charge B). The results of these calculations are illustrated in the diagram on the next slide with electric field vectors (EA and EB) drawn at a variety of locations. The strength of the field is represented by the length of the arrow and the direction of the field is represented by the direction of the arrow.
Continued… Since electric field is a vector, the usual operations that apply to vectors can be applied to electric field. That is, they can be added in head-to-tail fashion to determine the resultant or net electric field vector at each location. This is shown in the diagram below.
Continued… This shows that the magnitude and direction of the electric field at each location is simply the vector sum of the electric field vectors for each individual charge. If more locations are selected and the process of drawing EA, EB and Enet is repeated, then the electric field strength and direction at a multitude of locations will be known. (This is not done since it is a highly time intensive task.) Ultimately, the electric field lines surrounding the configuration of our two charges would begin to emerge. For the limited number of points selected in this location, the beginnings of the electric field line pattern can be seen. Note that for each location, the electric field vectors point tangent to the direction of the electric field lines at any given point.
Other Charge Configurations The construction of electric field lines in this manner is a tedious and cumbersome task. The use of a field plotting computer software program or a lab procedure produces similar results in less time. Whatever the method used to determine the electric field line patterns for a configuration of charges, the general idea is that the pattern is the resultant of the patterns for the individual charges within the configuration. The electric field line patterns for other charge configurations are shown in the diagrams below.
Unequal Amounts of Charge In each of the above diagrams, the individual source charges in the configuration possess the same amount of charge. Having an identical quantity of charge, each source charge has an equal ability to alter the space surrounding it. Subsequently, the pattern is symmetrical in nature and the number of lines emanating from a source charge or extending towards a source charge is the same. This reinforces a principle discussed earlier that stated that the density of lines surrounding any given source charge is proportional to the quantity of charge on that source charge. If the quantity of charge on a source charge is not identical, the pattern will take on an asymmetric nature, as one of the source charges will have a greater ability to alter the electrical nature of the surrounding space. This is depicted in the electric field line patterns on the next slide.
Review After plotting the electric field line patterns for a variety of charge configurations, the general patterns for other configurations can be predicted. There are a number of principles that will assist in such predictions. These principles are described (or re-described) in the list below. Electric field lines always extend from a positively charged object to a negatively charged object, from a positively charged object to infinity, or from infinity to a negatively charged object. Electric field lines never cross each other. Electric field lines are most dense around objects with the greatest amount of charge. At locations where electric field lines meet the surface of an object, the lines are perpendicular to the surface.
Electric Field Lines as an Invisible Reality It has been emphasized in Lesson 4 that the concept of an electric field arose as scientists attempted to explain the action-at-a-distance that occurs between charged objects. The concept of the electric field was first introduced by 19th century physicist Michael Faraday. It was Faraday's perception that the pattern of lines characterizing the electric field represents an invisible reality. Rather than thinking in terms of one charge affecting another charge, Faraday used the concept of a field to propose that a charged object (or a massive object in the case of a gravitational field) affects the space that surrounds it. As another object enters that space, it becomes effected by the field established in that space. Viewed in this manner, a charge is seen to interact with an electric field as opposed to with another charge. To Faraday, the secret to understanding action-at-a-distance is to understand the power of charge-field-charge. A charged object sends its electric field into space, reaching from the "puller to the pullee." Each charge or configuration of charges creates an intricate web of influence in the space surrounding it. While the lines are invisible, the affect is ever so real. So as you practice the exercise of constructing electric field lines around charges or configuration of charges, you are doing more than simply drawing curvy lines. Rather, you are describing the electrified web of space that will draw and repel other charges that enter it.
CYU #2 Erin Agin drew the following electric field lines for a configuration of two charges. What did Erin do wrong? Explain.
Answer #2 Electric field lines should never intersect each other. Erin crossed his lines.
CYU #3 Consider the electric field lines shown in the diagram below. From the diagram, it is apparent that object A is ____ and object B is ____. a. +, + b. -, - c. +, - d. -, + e. insufficient info
Answer #3 Answer: D Electric field lines are directed towards object A so object A must be negative. They are directed away from object B so object B must be positive.
CYU #4 Consider the electric field lines drawn below for a configuration of two charges. Several locations are labeled on the diagram. Rank these locations in order of the electric field strength - from smallest to largest.
Answer #4 Answer: DAECB (with the order of C and B being in question) Electric field strength is greatest where the lines are closest together and weakest where lines are furthest apart.
CYU #5 Use your understanding of electric field lines to identify the charges on the objects in the following configurations.
Answer #5 Answer: Objects A, C, F, G, H and I are positive. Objects B, D and E are negatively charged. The principle is: electric field lines always approach negatively charged objects and are directed away from positively charged objects.
Bell Work Describe the electric field strength at the six labeled locations of the irregularly shaped charged object below. Use the phrases "zero," "relatively weak," "moderate," and relatively strong" as your descriptions.
Bell work Answer A, F are relatively strong since they're the most pointed locations on the conductor's surface. B, E are relatively weak since they're at the least curved (most flat) locations on the conductor's surface. C is of moderate strength since it is at a location with some curvature but not an extreme amount. D is 0 since it is at a location under the surface of the conductor; electric fields are zero inside of conductors.
Electric Fields and Conductors
Physics Coach Stephens
Review Any charged object - positive or negative, conductor or insulator - creates an electric field that permeates the space surrounding it. In the case of conductors there are a variety of unusual characteristics about which we could elaborate: when a conductor acquires an excess charge, the excess charge distributes itself about the conductor to reduce the total amount of repulsive forces within it. We will explore this in more detail as we introduce the idea of electrostatic equilibrium. Electrostatic equilibrium is the condition established by charged conductors in which the excess charge has optimally distanced itself so as to reduce the total amount of repulsive forces. Once a charged conductor has reached the state of electrostatic equilibrium, there is no further motion of charge about the surface.
Electric Fields Inside of Charged Conductors Charged conductors that have reached electrostatic equilibrium share a variety of unusual characteristics: the electric field anywhere beneath the surface of a charged conductor is zero. Objects at electrostatic equilibrium have no further motion of charge about the surface. The electric field lines either begin or end upon a charge and in the case of a conductor, the charge exists solely upon its outer surface. The lines extend from this surface outward, not inward.
Electric Fields are Perpendicular to Charged Surfaces A second characteristic of conductors at electrostatic equilibrium is that the electric field upon the surface of the conductor is directed entirely perpendicular to the surface. There cannot be a component of electric field (or electric force) that is parallel to the surface. If the conducting object is a circle, then the perpendicular electric field vectors are aligned with the center of the sphere. If the object is irregularly shaped, then the electric field vector at any location is perpendicular to a tangent line drawn to the surface at that location.
Continued… The motion of electrons, like any physical object, is governed by Newton's laws. One outcome of Newton's laws was that unbalanced forces cause objects to accelerate in the direction of the unbalanced force and a balance of forces causes objects to remain at equilibrium. This truth provides the foundation for the rationale behind why electric fields must be directed perpendicular to the surface of conducting objects. If there were a component of electric field directed parallel to the surface, then the excess charge on the surface would be forced into accelerated motion by this component. Therefore, the electric field must be entirely perpendicular to the conducting surface for objects that are at electrostatic equilibrium.
Electric Fields & Surface Curvature A third characteristic of conducting objects at electrostatic equilibrium is that the electric fields are strongest at locations along the surface where the object is most curved. The curvature of a surface can range from absolute flatness on one extreme to being curved to a blunt point on the other extreme. A flat location has no curvature and is characterized by relatively weak electric fields. On the other hand, a blunt point has a high degree of curvature and is characterized by relatively strong electric fields. A sphere is uniformly shaped with the same curvature at every location along its surface. As such, the electric field strength on the surface of a sphere is the same everywhere.
Continued… To understand the rationale for this third characteristic, we will consider an irregularly shaped object that is negatively charged. Such an object has an excess of electrons. These electrons would distribute themselves in such a manner as to reduce the affect of their repulsive forces. Since electrostatic forces vary inversely with the square of the distance, these electrons would tend to position themselves so as to increase their distance from one another. On a regularly shaped sphere, the ultimate distance between every neighboring electron would be the same. But on an irregularly shaped object, excess electrons would tend to accumulate in greater density along locations of greatest curvature. Consider the diagram at the right. Electrons A and B are located along a flatter section of the surface.
Continued… Like all well-behaved electrons, they repel each other. The repulsive forces are directed along a line connecting charge to charge, making the repulsive force primarily parallel to the surface. On the other hand, electrons C and D are located along a section of the surface with a sharper curvature. These excess electrons also repel each other with a force directed along a line connecting charge to charge. But now the force is directed at a sharper angle to the surface. The components of the forces parallel to the surface are considerably less. A majority of the repulsive force between electrons C and D is directed perpendicular to the surface.
Continued… The parallel components of these repulsive forces are what cause excess electrons to move along the surface of the conductor. The electrons will move and distribute themselves until electrostatic equilibrium is reached. Once reached, the resultant of all parallel components on any given excess electron (and on all excess electrons) will add up to zero. All the parallel components of force on each of the electrons must be zero since the net force parallel to the surface of the conductor is always zero. For the same separation distance, the parallel component of force is greatest in the case of electrons A and B. So to acquire this balance of parallel forces, electrons A and B must distance themselves further from each other than electrons C and D. Electrons C and D on the other hand can crowd closer together at their location since that the parallel component of repulsive forces is less. In the end, a relatively large quantity of charge accumulates on the locations of greatest curvature. This larger quantity of charge combined with the fact that their repulsive forces are primarily directed perpendicular to the surface results in a considerably stronger electric field at such locations of increased curvature.
Check Your Understanding #1 Suppose that the sphere of a Van de Graaff generator gathers a charge. Then the motor is turned off and the sphere is allowed to reach electrostatic equilibrium. The charge ___. a. resides both on its surface and throughout its volume b. resides mostly inside the sphere and only emerges outside when touched c. resides only on the surface of the sphere
Answer #1 Answer: C When a "closed" conductor becomes charged, the excess of charge accumulates on the outer surface of the conductor. Since the generator has been turned off, there is no source of charge inside of it. All the charge resides on the outside of the dome.
CYU #3 A diagram of an irregularly shaped charged conductor is shown at the right. Four locations along the surface are labeled - A, B, C, and D. Rank these locations in increasing order of the strength of their electric field, beginning with the smallest electric field.
Answer #3 Answer: B < C < D < A For conducting surfaces, electric fields are strongest at locations where the curvature is the greatest. A projection (such as at point A) is the extreme case of lots of curvature. A flat section of a surface (such as point B) is on the opposite extreme with with no curvature. So point B is listed first and point A is listed last. Since point D is on a section of the surface which curves more than point C's section, the ordering of the final two locations is point C < point D.
CYU #4 Consider the diagram of the thumbtack shown at the right. Suppose that the thumbtack becomes positively charged. Draw the electric field lines surrounding the thumbtack.
Answer #4 The diagram was not created by a Field Plotting software program; it would certainly look better if it had been. Your answer may look different (especially when the details are compared) but it should share the following general characteristics with the diagram given here: The electric field lines should be directed from the positively charged thumbtack to the extremities of the page. Each field line MUST have an arrowhead on it to indicate such directions. All electric field lines should be perpendicular to the surface of the thumbtack at the locations where the lines and the thumbtack meet. There should be more lines concentrated at the pointed extremity of the thumbtack and the two sharply curved sections and fewer lines along the flatter sections of the thumbtack.
CYU #5 Diagram the electric field lines for the following configuration of two objects. Place arrows on your field lines.
Answer #5 Once more, the above diagram was not created by a Field Plotting software program; it would likely look better if it had been. Your answer may look different (especially when the details are compared) but it should share the following general characteristics with the diagram given here: The field lines should be directed from + to - or from the edge of the page to the - or from + to the edge of the page. Each field line MUST have an arrowhead on it to indicate such directions. At the surface of either object, the field lines should be directed perpendicular to the surface. There should be more lines at the sharply curved and pointed surfaces of the objects and less lines at the flatter sections.
CYU #6 TRUE or FALSE: Lightning rods are placed on homes to protect them from lightning. They work because the electric field is weak around the lightning rods; thus, there is little flow of charge between the lightning rods/home and the charged clouds.
Answer #6 Answer: False Electric fields are very strong along the sharply curved or blunt edges of lightning rod. This creates strong electric fields. To find out why they prevent lightning strikes, you'll have to read the next section of Lesson 4.
Physics Coach Stephens
Lightning Perhaps the most known and powerful display of electrostatics in nature is a lightning storm. Lightning storms are inescapable from humankind's attention. They are never invited, never planned and never gone unnoticed. The rage of a lightning strike will wake a person in the middle of the night. They send children rushing into parent's bedrooms, crying for assurance that everything will be safe. The fury of a lightning strike is capable of interrupting midday conversations and activities. They're the frequent cause of canceled ball games and golf outings. Children and adults alike crowd around windows to watch the lightning displays in the sky, standing in awe of the power of static discharges. Indeed, a lightning storm is the most powerful display of electrostatics in nature. In this part of Lesson 4, we will ponder two questions: What is the cause and mechanism associated with lightning strikes? How do lightning rods serve to protect buildings from the devastating affects of a lightning strike?
Static Charge Buildup in the Clouds The scientific community has long pondered the cause of lightning strikes. Even today, it is the subject of a good deal of scientific research and theorizing. The details of how a cloud becomes statically charged are not completely understood (as of this writing). Nonetheless there are several theories that make a good deal of sense and that demonstrate many concepts previously discussed in this unit of The Physics Classroom. The precursor of any lightning strike is the polarization of positive and negative charges within a storm cloud. The tops of the storm clouds are known to acquire an excess of positive charge and the bottoms of the storm clouds acquire an excess of negative charge. Two mechanisms seem important to the polarization process. One mechanism involves a separation of charge by a process that bears resemblance to frictional charging. Clouds are known to contain countless millions of suspended water droplets and ice particles moving and whirling about in turbulent fashion. Additional water from the ground evaporates, rises upward and forms clusters of droplets as it approaches a cloud. This upwardly rising moisture collides with water droplets within the clouds. In the collisions, electrons are ripped off the rising droplets, causing a separation of negative electrons from a positively charged water droplet or a cluster of droplets.
Second Mechanism The second mechanism that contributes to the polarization of a storm cloud involves a freezing process. Rising moisture encounters cooler temperatures at higher altitudes. These cooler temperatures cause the cluster of water droplets to undergo freezing. The frozen particles tend to cluster more tightly together and form the central regions of the cluster of droplets. The frozen portion of the cluster of rising moisture becomes negatively charged and the outer droplets acquire a positive charge. Air currents within the clouds can rip the outer portions off the clusters and carry them upward toward the top of the clouds. The frozen portion of the droplets with their negative charge tends to gravitate towards the bottom of the storm clouds. Thus, the clouds become further polarized.
Continued… These two mechanisms are believed to be the primary causes of the polarization of storm clouds. In the end, a storm cloud becomes polarized with positive charges carried to the upper portions of the clouds and negative portions gravitating towards the bottom of the clouds. The polarization of the clouds has an equally important affect on the surface of the Earth. The cloud's electric field stretches through the space surrounding it and induces movement of electrons upon Earth. Electrons on Earth's outer surface are repelled by the negatively charged cloud's bottom surface. This creates an opposite charge on the Earth's surface. Buildings, trees and even people can experience a buildup of static charge as electrons are repelled by the cloud's bottom. With the cloud polarized into opposites and with a positive charge induced upon Earth's surface, the stage is set for Act 2 in the drama of a lightning strike.
The Mechanics of a Lightning Strike As the static charge buildup in a storm cloud increases, the electric field surrounding the cloud becomes stronger. Normally, the air surrounding a cloud would be a good enough insulator to prevent a discharge of electrons to Earth. Yet, the strong electric fields surrounding a cloud are capable of ionizing the surrounding air and making it more conductive. The ionization involves the shredding of electrons from the outer shells of gas molecules. The gas molecules that compose air are thus turned into a soup of positive ions and free electrons. The insulating air is transformed into a conductive plasma. The ability of a storm cloud's electric fields to transform air into a conductor makes charge transfer (in the form of a lightning bolt) from the cloud to the ground (or even to other clouds) possible.
Step Leader A lightning bolt begins with the development of a step leader. Excess electrons on the bottom of the cloud begin a journey through the conducting air to the ground at speeds up to 60 miles per second. These electrons follow zigzag paths towards the ground, branching at various locations. The variables that affect the details of the actual pathway are not well known. It is believed that the presence of impurities or dust particles in various parts of the air might create regions between clouds and earth that are more conductive than other regions. As the step leader grows, it might be illuminated by the purplish glow that is characteristic of ionized air molecules. Nonetheless, the step leader is not the actual lightning strike; it merely provides the roadway between cloud and Earth along which the lightning bolt will eventually travel.
Streamer As the electrons of the step leader approach the Earth, there is an additional repulsion of electrons downward from Earth's surface. The quantity of positive charge residing on the Earth's surface becomes even greater. This charge begins to migrate upward through buildings, trees and people into the air. This upward rising positive charge - known as a streamer- approaches the step leader in the air above the surface of the Earth. The streamer might meet the leader at an altitude equivalent to the length of a football field. Once contact is made between the streamer and the leader, a complete conducting pathway is mapped out and the lightning begins. The contact point between ground charge and cloud charge rapidly ascends upward at speeds as high as 50 000 miles per second. As many as a billion trillion electrons can transverse this path in less than a millisecond. This initial strike is followed by several secondary strikes or charge surges in rapid succession. These secondary surges are spaced apart so closely in time that may appear as a single strike. The enormous and rapid flow of charge along this pathway between the cloud and Earth heats the surrounding air, causing it to expand violently. The expansion of the air creates a shockwave that we observe as thunder.
Lightning Rods & Other Protective Measures Tall buildings, farmhouses and other structures susceptible to lightning strikes are often equipped with lightning rods. The attachment of a grounded lightning rod to a building is a protective measure that is taken to protect the building in the event of a lightning strike. The concept of a lightning rod was originally developed by Ben Franklin. Franklin proposed that lightning rods should consist of a pointed metal pole that extends upward above the building that it is intended to protect. Franklin suggested that a lightning rod protects a building by one of two methods. First, the rod serves to prevent a charged cloud from releasing a bolt of lightning. And second, the lightning rod serves to safely divert the lightning to the ground in event that the cloud does discharge its lightning via a bolt. Franklin's theories on the operation of lightning rods have endured for a couple of centuries. And not until the most recent decades have scientific studies provided evidence to confirm the manner in which they operate to protect buildings from lightning damage.
Lightning Dissipation Theory The first of Franklin's two proposed theories is often referred to as the lightning dissipation theory. According to the theory, the use of a lightning rod on a building protects the building by preventing the lightning strike. The idea is based upon the principle that the electric field strength is great around a pointed object. The intense electric fields surrounding a pointed object serve to ionize the surrounding air, thus enhancing its conductive ability. The dissipative theory states that as a storm cloud approaches, there is a conductive pathway established between the statically charged cloud and the lightning rod. According to the theory, static charges gradually migrate along this pathway to the ground, thus reducing the likelihood of a sudden and explosive discharge. Proponents of the lightning dissipation theory argue that the primary role of a lightning rod is to discharge the cloud over a longer length of time, thus preventing the excessive charge buildup that is characteristic of a lightning strike.
Continued… The second of Franklin's proposed theories on the operation of the lightning rod is the basis of the lightning diversion theory. The lightning diversion theory states that a lighting rod protects a building by providing a conductive pathway of the charge to the Earth. A lightning rod is typically attached by a thick copper cable to a grounding rod that is buried in the Earth below. The sudden discharge from the cloud would be drawn towards the elevated lightning rod but safely directed to the Earth, thus preventing damage from occurring to the building. The lightning rod and the attached cable and ground pole provide a low resistance pathway from the region above the building to the ground below. By diverting the charge through the lightning protection system, the building is spared of the damage associated with a large quantity of electric charge passing through it.
Continued… Lightning researchers are now generally convinced that the lightning dissipation theory provides an inaccurate model of how lightning rods work. It is indeed true that the tip of a lightning rod is capable of ionizing the surrounding air and making it more conductive. However, this affect only extends for a few meters above the tip of the lightning rod. A few meters of enhanced conductivity above the tip of the rod is not capable of discharging a large cloud that stretches over several kilometers of distance. Unfortunately, there are currently no scientifically verified methods of lightning prevention. Furthermore, recent field studies have further shown that the tip of the lightning rod does not need to be sharply pointed as Ben Franklin suggested. Blunt-tipped lightning rods have been found to be more receptive to lightning strikes and thus provide a more likely path of discharge of a charged cloud. When installing a lightning rod on a building as a lightning protection measure, it is imperative that the rod be elevated above the building and connected by a low resistance wire to the ground.
Check Your Understanding #1 TRUE or FALSE: The presence of lightning rods on top of buildings prevents a cloud with a static charge buildup from releasing its charge to the building.
Answer #1 Answer: FALSE Contrary to a commonly held belief, a lightning rod does not serve to prevent a lightning bolt. The presence of the rod on the building can only serve to divert the charge in the bolt to the ground through a low resistance pathway and thus protect the building from the damage which would otherwise result.
CYU #2 TRUE or FALSE: If you place a lightning rod on top of your home but failed to ground it, then it is unlikely that your home would be struck by lightning.
Answer #2 Answer: False The presence of an elevated lightning rod would serve to draw charge from the cloud to the ground. In the event of a lightning strike, a bolt would likely select a path from the cloud that ultimately connects to the rod. If the rod is not grounded, then the charge would likely pass through the home during its journey to the ground. The intense heat associated with the lightning bolt would cause severe damage and possibly cause an explosion or a fire. In the end, it would have been better to not even have installed a lightning rod than to have installed one that is not grounded.
Review Session Static Electricity Multimedia: Charging a Single Sphere by Induction Using a Negatively-Charged Object Charging a Two-Sphere System by Induction Using a Negatively-Charged Object Charging an Electrophorus Plate by Induction Using a Negatively-Charged Object Charging an Electroscope by Induction Using a Negatively-Charged Object Grounding a Positively-Charged Electroscope Grounding a Negatively-Charged Electroscope Static Electricity Photos: http://www.physicsclassroom.com/gallery/estatics/ Reasoning Center Questions: http://www.physicsclassroom.com/reasoning/electrostatics/ Mind on Physics Internet Modules: http://www.physicsclassroom.com/mop/module.cfm Static Electricity Problem Set: http://www.physicsclassroom.com/calcpad/estatics/
Homework 2/19 – 2/22 Due Friday! Electric Field Worksheet -- http://www.physicsclassroom.com/curriculum/estatics/static8.pdf Electric Field Lines Worksheet– http://www.physicsclassroom.com/curriculum/estatics/static9.pdf Static Electricity Review Questions – http://www.physicsclassroom.com/reviews/estatics/estaticsprint.cfm Review Question Answers – http://www.physicsclassroom.com/reviews/estatics/estaticsans.cfm