23 Faradays Law and Inductance 23 1 Faradays

23. Faraday’s Law and Inductance 23 -1. Faraday’s Law of Induction (p 852) • Electric current is induced by the change of the Magnetic Flux Unit : weber (Wb) 1 Wb = 1 T·m 2 • An Emf induced in a circuit the time rate of change of magnetic flux though the circuit. For N loops 1

23 -2. Motional emf (p 859) Magnetic Force Charge accumulated at the ends until Fm = -Fe Potential difference Equivalent Circuit const. v 2

Example 23 -3 emf induced in a Rotating Bar • The Alternating-Current (AC) Generator (p 862) N-coils max (ε max = BAN ) t - max AC-Voltage 3

23 -3. Lenz’s Law (p 863) The magnetic field due to the induced current has opposite sign to the change in the magnetic flux. 4

23 -4. Induced emf and Electric Fields (p 867) Assume the magnetic field changes in time r Conducting Loop (e. g; Copper wire ring) Does not need presence of charges! There is no beginning or end, complete loop! This is different from “Electrostatics”! Faraday’s Law 5

23 -5. Self-Inductance (p 869) B-field I L: Self-Inductance Unit : Henry (H) i (increase) i (decrease) - L L : Against the increase of the current 6

The self-inductance of a devise depends on its geometry. Inductance of Solenoid Inductance in Series: Inductance in Parallel: i 1 L 1 i i i 2 L 2 ; Same as in the case of resistance 7

23 -6. Circuits (p 872) resistance capacitance A. RC Circuit Inductance (ref. 21 -9) 1. + C - + - 2 R 1 S 2. Q C I t i 0= /R t -i 0 8

B. RL Circuit 1. R L + - 2 1 S at t =0 2. i /R t 1 t 2 t 9

23 -7. Energy Stored in a Magnetic Field (p 876) Cf ) Energy stored in a capacitor In LR Circuit + - R L Power: In a solenoid (Magnetic Energy) A l (Magnetic energy density) Cf) (Electric energy density) Ch-23 H. W. ; 12, 15, 22, 24, 37, and 61 10