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Dr. Jie ZouPHY 13611 Chapter 31 Faraday’s Law

Dr. Jie ZouPHY 13612 Outline Faraday’s law of induction Some observations and Faraday’s experiment Faraday’s law of induction Some applications of Faraday’s law of induction: An electric guitar Motional emf

Dr. Jie ZouPHY 13613 Some observations Observations: (a) When a magnet is moved toward a loop of wire connected to a galvanometer, the galvanometer deflects, indicating an induced current in the loop. (b) When the magnet is held stationary, there is no induced current in the loop, even when the magnet is inside the loop. (c) When the magnet is moved away from the loop, the galvanometer deflects in the opposite direction, indicating an induced current opposite that in part (a). A current is set up even though no batteries are present in the circuit! Such a current is called an induced current and it is produced by an induced emf.

Dr. Jie ZouPHY 13614 Faraday’s experiment Observations: (1) At the instant the switch is closed, the galvanometer needle deflects in one direction and then returns to zero. (2) At the instant the switch is opened, the needle deflects in the opposite direction and again returns to zero. (3) The galvanometer reads zero when there is either a steady current or no current in the primary circuit. Faraday’s conclusion: An electric current can be induced in a circuit by a changing magnetic field. An induced emf is produced in the secondary circuit by the changing magnetic field.

Dr. Jie ZouPHY 13615 Faraday’s law of induction Faraday’s law of induction: The emf induced in a circuit is directly proportional to the time rate of change of the magnetic flux through the circuit. Here, is the magnetic flux through the circuit. (1) For a planar loop in a uniform magnetic field: (2) For a coil consisting of N loops:

Dr. Jie ZouPHY 13616 Applications of Faraday’s law An electric guitar

Dr. Jie ZouPHY 13617 Examples Example 31.1: A coil consists of 200 turns of wire. Each turn is a square of side 18 cm, and a uniform magnetic field directed perpendicular to the plane of the coil is turned on. If the field changes linearly from 0 to 0.50 T in 0.80 s, (a) what is the magnitude of the induced emf in the coil while the field is changing? (b) If the ends of the coil are connected to a circuit and the total resistance is 2.0 , what is the current in the coil? Example 31.2: A loop of wire enclosing an area A is placed in a region where the magnetic field is perpendicular to the plane of the loop. The magnitude of B varies in time according to B = B max e -at, where a is some constant. Find the induced emf in the loop as a function of time.

Dr. Jie ZouPHY 13618 Motional emf Motional emf: The emf induced in a conductor moving through a constant magnetic field. Consider a straight conductor of length l moving with a velocity v through a uniform magnetic field B directed perpendicular to v: |  | = Blv I = Blv/R If v is constant, power delivered by the applied force = power delivered to the resistor=  2 /R = B 2 l 2 v 2 /R.

Dr. Jie ZouPHY 13619 Examples Example 31.4: A conducting bar of length l rotates with a constant angular speed  about a pivot at one end. A uniform magnetic field B is directed perpendicular to the plane of rotation. Find the motional emf induced between the ends of the bar. Example 31.5: The conducting bar moves on two frictionless parallel rails in the presence of a uniform magnetic field directed into the page. The bar has mass m and its length is l. The bar is given an initial velocity v i to the right and is released at t = 0. Using Newton’s laws, find the velocity of the bar as a function of time.

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