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Dr. Jie ZouPHY 13611 Chapter 31 Faraday’s Law (Cont.)

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Dr. Jie ZouPHY 13612 Outline Lenz’s law Induced emf and electric fields Maxwell equations Generators and motors

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Dr. Jie ZouPHY 13613 Lenz’s law Lenz’s law: The induced current in a loop is in the direction that creates a magnetic field that opposes the change in magnetic flux through the area enclosed by the loop. The induced current tends to keep the original flux through the circuit from changing. Examples

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Dr. Jie ZouPHY 13614 More examples Q1: Assume that the battery in the figure is replaced by an AC source and the switch is held closed. Will there be an induced current in the metal ring, if so, what will be the direction. Q2: A bar magnet is held above a loop of wire in a horizontal plane. The south end of the magnet is toward the loop of wire. The magnet is dropped toward the loop. Find the direction of the current through the resistor (a) while the magnet is falling toward the loop and (b) after the magnet has passed through the loop and moves away from it.

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Dr. Jie ZouPHY 13615 Induced emf and electric fields We can relate an induced current in a conducting loop to an electric field by claming that an electric field is created in the conductor as a result of the changing magnetic flux. Since the existence of an electric field is independent of the presence of any test charges, this suggests that even in the absence of a conducting loop, a changing magnetic field would still generate an electric field in empty space. Faraday’s law in general form: The induced electric field E in the above equation is a nonconservative field that is generated by a changing magnetic field.

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Dr. Jie ZouPHY 13616 Maxwell’s equations Maxwell’s equations: Developed by James Clerk Maxwell; Include four equations that are regarded as the basis of all electrical and magnetic phenomena. The four equations are: Lorentz force law: F = qE + qv B Gauss’s law Gauss’s law in magnetism Faraday’s law Ampère- Maxwell law

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Dr. Jie ZouPHY 13617 Generators and motors An alternating current (AC) generator (left) and a simple electric motor (right)

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General electric flux definition

General electric flux definition

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