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Finishing Up. Electricity, Magnetism and some applications to music. SURVEY First. Exam in this room. Bring Pencils and SCANTRONs. Calendar. Schedule. This week we take a quick look at electricity and magnetism and applications to music Read in Textbook: (Mostly Qualitative)
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Finishing Up Electricity, Magnetism and some applications to music
Exam in this room. Bring Pencils and SCANTRONs
Schedule • This week we take a quick look at electricity and magnetism and applications to music • Read in Textbook: (Mostly Qualitative) • Chapter 20: 402-407, 411-412, 414-420 • Chapter 21: 427-432, 433-436 • Chapter 22: 446-451, • Read in Measured Tones • 268-2748, 281-284,173,178, (mostly qualitative/historical) • Last WebAssign has been posted • We are almost there!
Introduction • The early Greeks knew that amber—a fossilized tree sap currently used in jewelry—had the interesting ability to attract bits of fiber and hair after it was rubbed with fur. This was one way of recognizing an object that was electrified. • In modern terminology we say the object is charged. • This doesn’t explain what charge is, but is a handy way of referring to this condition.
Idiot! If lightening had actually traveled down the kite string, old Ben Franklin would have been toast! Probably never happened, but good story!
Demonstration Procedure Pivot • The sequence of Experiments • Identify two rods • Treat each rod • Bring one rod near to the other • Observe what happens • See what we can learn
If you rubbed the rods longer and/or harder, do you think the effect that you see would be • Stronger • Weaker • The same
If the two rods are brought closer together, the force acting between them will get … Stronger Weaker The same
Definition of sorts We DEFINE the “stuff” that we put on the rods by the rubbing process as CHARGE. We will try to understand what charge is and how it behaves. We add to the properties of materials: Mass Charge
What’s Going On? • All of these effects involve rubbing two surfaces together. • Or pulling two surfaces apart. • Something has “happened “to each of these objects. • These objects have a new PROPERTY • Other properties are mass, color • We call this NEW PROPERTY .………. ………CHARGE. • There seems to be two types of charge.
We call these two types of charge • Positive • Negative An object without either a (+) or (-) charge is referred to as being NEUTRAL.
An Example Volunteer Please
We have also observed that there must be TWO kinds of charge. • Call these two types • positive (+) • negative(-) • We “define” the charge that winds up on the rubber rod when rubbed by the dead cat to be NEGATIVE. • The charge on the glass rod or the dead cat is consequently defined as POSITIVE.
Old Ben screwed up more than once!! ++++++++++--------- ----+++---++---+-++-??
From whence this charge??? Easily Removed - +
The nucleus of a certain type of neon atom contains 10 protons and 10 neutrons. What is the total charge of the nucleus?
Materials • Conductors • Charge easily moves in conducting materials • Usually metals … Cu, Ag, Al, Au, etc. • Insulators • Charge does NOT move • Others • Semiconductors – Transistors, etc. • Semimetals – Don’t ask!
Electrical Properties • Why doesn’t the charge flow to ground through our bodies? • It stays on the rod because the rod is an insulator; charge generated at one end remains there. • The charge can be removed by moving our hands along the charged end. • As we touch the regions that are charged, the charges flow through our bodies to ground.
Electrical Properties • A metal rod cannot be charged by holding it in our hands and rubbing it with a cloth because metal conducts the charge to our hands. • A metal rod can be charged if it is mounted on an insulating stand or if we hold it with an insulating glove; that is, the rod must be insulated from its surroundings.
Conservation of Charge • Like Gilbert, Benjamin Franklin believed that electricity was a single fluid and that an excess of this fluid caused one kind of charged state, whereas a deficiency caused the other. • Because he could not tell which was which, he arbitrarily named one kind of charge positive and the other kind negative. • By convention the charge on a glass rod rubbed with silk or plastic film is positive, whereas that on an amber or rubber rod rubbed with wool or fur is negative.
Conservation of Charge • In our modern physics world view, all objects are composed of negatively charged electrons, positively charged protons, and uncharged neutrons. • The electron’s charge and the proton’s charge have the same size. • An object is uncharged (or neutral) because it has equal amounts of positive and negative charges, not because it contains no charges. • For example, atoms are electrically neutral because they have equal numbers of electrons and protons.
Conservation of Charge • Positively charged objects may have an excess of positive charges or a deficiency of negative charges; that is, an excess of protons or a deficiency of electrons. We simply call them positively charged because the electrical effects are the same in both situations. • The modern view easily accounts for the conservation of charge when charging objects. • The rubbing simply results in the transfer of electrons from one object to the other; whatever one object loses, the other gains.
The Electric Force • Simple observations of the attraction or repulsion of two charged objects indicate that the size of the electric force depends on distance. • For instance, a charged object has more effect on an electroscope as it gets nearer. • But we need to be more precise. • How does the size of this force vary as the separation between two charged objects changes? • And how does it vary as the amount of charge on the objects varies?
The Electric Force • In 1785 French physicist Charles Coulomb measured the changes in the electric force as he varied the distance between two objects and the charges on them. • He verified that if the distance between two charged objects is doubled (without changing the charges), the electric force on each object is reduced to one-fourth the initial value. • If the distance is tripled, the force is reduced to one-ninth, and so on. • This type of behavior is known as an inverse-square relationship; inverse because the force gets smaller as the distance gets larger, square because the force changes by the square of the factor by which the distance changes.
The Electric Force • Coulomb also showed that reducing the charge on one of the objects by one-half reduced the electric force to one-half its original value. • Reducing the charge on each by one-half reduced the force to one-fourth the original value. • This means that the force is proportional to the product of the two charges. • These two effects are combined into a single relationship known as Coulomb’s law: • In this equation, q1 and q2 represent the amount of charge on objects 1 and 2, r is the distance between their centers, and k is a constant (known as Coulomb’s constant) whose value depends on the units chosen for force, charge, and distance.
The Electric Force • Each object feels the force due to the other. The forces are vectors and act along the line between the centers of the two objects. The force on each object is directed toward the other if the charges have opposite signs and away from each other if the charges have the same sign. • Because the two forces are due to the interaction between the two objects, the forces are an action– reaction pair. According to Newton’s third law, the forces are equal in magnitude, point in opposite directions, and act on different objects.
The Electric Force • Because the existence of an elementary, fundamental charge was not known until the 20th century, the unit of electric charge, the coulomb (C), was chosen for convenience in use with electric circuits. (We will formally define the coulomb later.) • Using the coulomb as the unit of charge, the value of Coulomb’s constant is determined by experiment to be:
The Electric Force • The coulomb is a tremendously large unit for the situations we have been discussing. For instance, the force between two spheres, each having 1 coulomb of charge and separated by 1 meter, is: • This is a force of 1 million tons!
The Electric Field • Implicitly, we have assumed the force between two charges to be the result of some kind of direct interaction—sort of an action-at-a-distance interaction. • This type of interaction is a little unsettling because there is no direct pushing or pulling mechanism in the intervening space. • Electrical effects are evident even in situations in which there is a vacuum between the charges. • If this were the only purpose of the field idea, it would play a minor role in our physics world view. • In fact, it probably seems like we are trading one unsettling idea for another. • However, as we continue our studies, we will find that the electric field takes on an identity of its own. As we will learn in Chapter 22, electric and magnetic fields can travel through space as waves.
The Electric Field • We define the electric field E at every point in space as the force exerted on a unit positive charge placed at the point. • This is equivalent to the way that the gravitational field was defined, with the unit mass replaced by a unit positive charge. • Because force is a vector quantity, the electric field is a vector field; it has a size and a direction at each point in space. • You could imagine the space around a positive charge as a “porcupine” of little arrows pointing outward, as shown in figure to the left. • The arrows farther from the charge would be shorter to indicate that the force is weaker there.
The Electric Field • The values for an actual electric field can be measured with a test charge. • The unit of charge that we have been using is 1 coulomb. • This is a very large amount of charge, and if we actually used 1 coulomb as our test charge, it would most likely move the charges that generated the field, thus disturbing the field. • Therefore, we use a much smaller charge, such as 1 microcoulomb, and obtain the size of the field by dividing the measured force F by the size q of the test charge: • Notice that the units of electric field are newtons per coulomb (N/C).
The Electric Field • If we know the sizes and locations of the charges creating the electric field, we can also calculate the value of the field at any point of interest by assuming that we place a 1 coulomb charge at the location and calculating the force on this charge using Coulomb’s law. • In doing this, we can take advantage of the fact that each charge acts independently; the effects simply add. • This means that we calculate the contribution of each charge to the field and then add these contributions vectorially.
The Electric Field • Once we know the value of the electric field at any point, we can calculate the force that any charge q would experience if placed at that point: • This is read as, “The force on an object is equal to the net charge q on the object times the electric field E at the location of the object.”
The Electric Field • As an example, let’s assume that we have generated a uniform electric field that points downward and has a size of 1000 newtons per coulomb. If we place an object in this field that has a positive charge of 1 microcoulomb, the object will experience a downward force of: • If we change the charge on the object, it is very easy to calculate the new force; we do not have to deal with the charges that produced the electric field.
What is the electric field at a distance of 1 m from a 1 C charge? • Imagine a UNIT charge (1 coulomb) placed at the point where we want to know the electric field. • Calculate the FORCE on the unit charge • The Electric Field is then
Electric Potential • Because objects with different charges have different electric potential energies at a given point, it is often more convenient to talk about the energy available due to the electric field without reference to a specific charged object. • The electric potential V at each point in an electric field is defined as the electric potential energy EPE divided by the object’s charge q:
Electric Potential • Notice that it doesn’t matter which charged object we use to define the electric potential. • This quantity is numerically equal to the work required to bring a positive test charge of 1 coulomb from the zero reference point to the specified point. • The units for electric potential are joules per coulomb (J/C), a combination known as a volt (V). • Because of this, we often speak of the electric potential as a voltage. • If you have a potential difference across a conducting material, you will have a motion of electrons. This motion of charge is called a CURRENT and is measured in Coulombs per second. • 1 C/sec is defined as a current of 1 AMPERE
Current has to have a PLACE to go! No Light
A “Complete” Circuit “Let there be Light” Current I I~V V
The Constant • I~V • V=IR (R is proportionality constant) • R is a property of the material • Some Materials are more “resistive to” the flow of current. • R is called the resistance. • Units: Volts/Ampere = OHMs
