Unit 6 Fields • This unit uses the concept of fields to explain the behavior of electric and magnetic forces. The interaction of electric and magnetic fields is examined as well as how these interactions can be used for a number of practical applications.
Module 6.1 – Electric Fields • This module begins with an introduction to static electricity and some basic electrical concepts. It goes on to study the mathematical relationship governing electrical forces and uses field theory to explain this phenomenon. The module concludes with an introduction to electric potential difference, which is the basis for understanding electric current.
Static Electricity • Law of conservation of electric charge – when charging objects by rubbing, the net change in the amount of charge is zero • Structure of the atom consists of a positively charged nucleus that is surrounded by one or more negatively charged electrons • Only electrons move in solid objects
Static Electricity • Ion – an atom which has gained or lost an electron • Elementary charge – the magnitude of the charge on an electron or proton • Conductor is a material in which many of the electrons are bound very loosely to the nuclei and can move about freely within the material • Insulator is a material in which there are almost no loosely bound electrons
Ways to Charge an Object • Friction – objects can be charged by rubbing them together to exchange charge • Conduction – electrons are transferred to or from a charged object to a neutral object • Induction - charged object does not actually touch the neutral one, but is just brought near it. This causes the electrons in the neutral object to redistribute themselves
Electroscope Negative Charge Neutral Induced Charge
Check Your Learning • An object that has a net excess charge of 5 positive elementary charges is picked up by a student and becomes neutral. What is the best hypothesis to explain this change in charge condition? • The object gained 5 electrons from the student. • The object gained 5 protons from the student. • The object lost 5 electrons to the student. • The object lost 5 protons to the student. a - Protons do not get transferred between solid objects. Since the object became less positive, it must have gained electrons.
Check Your Learning • Object A is repelled from object B. Object C is attracted to object B. If A is negative, C is • Positive • Positive or neutral • Negative • Negative or neutral b – Since A is negative, B must also be negative (since it was repelled). Since C was attracted to B, it could be positive or neutral (since a neutral object could be attracted through induction)
Check Your Learning • If you move a charged rod toward a positively charged electroscope, the leaves at first collapse and then diverge. What charge is on the rod? The rod must have been negatively charged. A negatively charged rod will repel electrons into the positively charged leaves, making them neutral so that they will collapse. If the rod is strongly negative, it can continue to repel electrons into the leaves so that they are now negatively charged and will diverge again.
Check Your Learning • Distinguish between charging by induction and charging by conduction. Charging by conduction involves making contact between the charged object and the object to be charged, so that electrons can actually flow from one to the other; charging by induction involves bringing the charged object close to the object to be charged so that electrons are simply repositioned within the object to be charged - no electrons are transferred from the charged object to the object to be charged.
Coulomb’s Law Measured in coulombs (C) Measured in metres (m)
Coulomb’s Law • Similar to Universal Gravitation! microcoulomb Elementary charge
Example Calculate the electrical force between a -34.2 μC charge and a +46.8 μC charge if they are 2.1 cm apart. Is it attractive or repulsive?
Solution • Since the two charges are oppositely charged (one negative and one positive), the force is attractive.
Check Your Learning How far apart are two electrons if they exert a force of repulsion of 1.0 N on each other?
Electric Field • Electric Field is defined as • Direction is defined as the direction of the force on a positive test charge • Measured in N/C
Electric Field • For the electric field due to a point source • For multiple point sources,
Example What is the electric field 2.0 cm away from a 1.0 μC charged particle? • Since the source is positive, the force on a positive test charge would be away from the source, or outward.
Drawing Electric Fields • To visualize an electric field, draw a series of lines to indicate the direction of the electric field at various points in space • For a positive point source,
Drawing Electric Fields • For multiple charges Electric Field Simulator
Drawing Electric Fields The lines of force in an electric field diagram do a number of things: • They indicate the direction of the electric field; • They are drawn so that the magnitude of the electric field is proportional to the number of field lines in a unit area. The closer together the field lines, the stronger the electric field. Note in our diagrams above that the lines are closer together near the charges than they are further away from the charges. This tells us that the electric field is stronger near the charges.
Gravitational Fields • Field Concept can be extended to gravity or
Check Your Learning • You are probing the field of a charge of unknown magnitude and sign. You first map the field with a 1.0 μC test charge, then repeat your work with a 2.0 μC charge. • Would you measure the same forces with the two test charges? Explain. No, you would not. Since the force depends on both of the charges, changing either charge will change the force. • Would you find the same fields? Explain. Yes, you would find the same field. The field depends only on the source charge, not the test charge.
Check Your Learning • A negative charge of 0.020 μC experiences a force of 0.060 N to the right in an electric field. What is the field magnitude and direction? Since the charge is the one experiencing the force due to an electric field, it is a test charge. Since the force on the negative test charge is to the right, the force on a positive test charge would be to the left
Electric Potential Energy • q has potential energy – it will move to the left if released • To increase potential energy, must do work by moving it to the right
Electric Potential Energy • q has potential energy – it will move to the right if released • To increase potential energy, must do work by moving it to the left
Electric Potential Energy • If you must do work against the electric field to move the charge, you are increasing the potential energy of the system. • If the electric field is doing work on the charge, than the potential energy of the system is decreasing. In this case, the kinetic energy of the charge will increase.
Electric Potential • Electric Potential is defined as the potential energy per unit charge: • Since potential energy (hence potential) can only be measured relative to some reference point, potential difference defined as or
Example 1 An electron in a picture tube of a TV set is accelerated from rest through a potential difference of 5.00 ×103 V. What is the speed of the electron as a result of this acceleration?
Example 1 So the electron lost 8.00 ×10-16 J of potential energy. Conservation of energy tells us that it must have gained the same amount of kinetic energy.
Sharing Charge • All systems come to equilibrium when the energy of the system is at a minimum. • For example, a ball on a hill will come to rest in the valley below where the potential energy is a minimum • Consider two spheres, one negatively charged (A) and one neutral (B). Since the excess electrons are being held close together on sphere A, we say that it is at a high potential; sphere B is said to be neutral. • Electrons will go from sphere A into sphere B until the potentials are equal
Equipotential Lines • An equipotential line is one in which all of the points are at the same potential; that is, the potential difference between any two points on the line is zero • Equipotential lines are perpendicular to the electric field at any point; if not, work would be required to move the charge along the surface against this electric field.
Uniform Electric Fields • Consider two oppositely charged parallel plates • Electric field lines in between these plates are parallel and evenly spaced, indicating a uniform electric field
Uniform Electric Field • To push a positively charged particle from point a to point b will require a constant force since the electric field is uniform
Example 2 A voltmeter reads 500. V when placed across two charged, parallel plates. The plates are 2.0 cm apart. What is the magnitude of the electric field between them?
Check Your Learning The work done by an external force to move a -7.50 μC charge from point a to point b is 2.50 ×10-3 J. If the charge was started from rest and had 4.82 × 10-4 J of kinetic energy when it reached point b, what must be the potential difference between a and b?
Module Summary In this module you learned that • Static electricity is a result of interaction between electrons and protons. • The force between electric point charges is given by Coulomb’s Law • An electric field is a concept used to help us understand the behavior of electric charges and is defined as
Module Summary • The magnitude of an electric field due to a point source is given by • Electric fields and electric potential can be represented visually using lines of force and equipotential lines. • The electrical potential difference between two points is defined by • The potential difference between two points in a uniform electric field is given by
Module 6.2 – Electric Current This module introduces the concept of electric current and its relationship to electric potential difference and resistance. The relationship between electricity and power is examined, including how electrical energy is calculated and paid for. The remainder of this unit deals with various types of electrical circuits and how to analyze these circuits.
Current • Current is a flow of electrons through a conductor as a result of a potential difference • Current (I) defined as the rate of flow of charge • Current is measured in amps – 1 A= 1 C/s • Conventional Current – refers to the “flow” of positive charge, not electrons
Example 1 A service station charges a battery using a current of 5.5 A for 6.0 h. How much charge passes through the battery?
Potential Difference • Required for a current to flow • Charge flows from a higher potential to a lower potential • Example: • Water pipe with water in it is held horizontal • By lifting one end, you increase the potential • Higher the end is lifted, the more water that flows • Flow of water is similar to the current
Resistance • More resistance reduces flow of current • Measured in ohms (Ω) • Charges lose potential when traveling through a resistance • Resistance depends on • Type of material • Temperature • Thickness • Length
Resistance • Resistance has been shown experimentally to be calculated using • ρ is the resistivity and is measured in Ω·m • Resistivity depends on the material being used (and temperature)
Example 2 Suppose that you want to connect your stereo to a set of speakers. If each wire must be 18.0 m long, what diameter silver wire must be used so that the resistance of each wire is less than 0.12 Ω.
Ohm’s Law • Ohm's Law – discovered experimentally by Georg Ohm to apply to many materials. • In materials that follow Ohm's Law, the current is proportional to the voltage. • resistance must therefore be constant. • Most (but not all) metals obey Ohm's Law. A resistor that follows Ohm's law is said to be ohmic.
Ohm’s Law • Current, potential difference, and resistance are related by • unit of resistance is defined so that 1 Ω= 1 V/A. • Ohm's Law refers to the fact that the resistance for most conductors does not depend on the potential difference across the conductor