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Faraday’s Law 3 m/s 2 m 10 m 5 T 10  What is the current induced in this circuit?   C)10A D) 6A

Faraday’s Law 3 m/s 2 m 10 m 5 T 10  As the bar moves a current is induced! There are no batteries anywhere, so we say that a current is induced, by an induced emf. Hence, an electric current can be induced in a circuit by a changing magnetic field, in the opposite direction to the change in flux.

Comparision of Induction No magnetic monopole, hence no magnetic current Electric fields and magnetic fields induce in opposite fashions

Faraday’s Law and Electric Fields. A cylindrical region of radius R = 3.0 cm contains a uniform magnetic field parallel to its axis. The field is 0 outside the cylinder. If the field is changing at the rate 0.60 T/s, the electric field induced at a point 2R from the cylinder axis is: Using Faraday’s law: 2  (2R)E =-  (R 2 ) dB/dt, so E= (-(R 2 ) /4) dB/dt= V/m

Maxwell’s Equations Integral Form Gauss’s laws, Ampere’s law and Faraday’s law all combined! They are nearly symmetric with respect to magnetism and electricity. The lack of magnetic monopoles is the main reason why they are not completely symmetric.

Quiz The diagrams show three circuits with identical batteries, identical inductors, and identical resistors. Just after the switch is closed which has the least current through the battery? The diagrams show three circuits with identical batteries, identical inductors, and identical resistors. Just after the switch is closed which has the greatest current through the battery? The diagrams show three circuits with identical batteries, identical inductors, and identical resistors. A very long time later, which has the least current through the battery?

RL - Circuits EE – + What happens when the switch S is closed at t = 0? R L S Let I be the current in the circuit I Use Kirchoffs rule for loops on the circuit

RC–Circuits vs RL-Circuits At t=0, ordinary wire As t-> infinity, broken wire At t=0, broken wire, little current for small t As t-> infinity, ordinary wire In terms of current control, an inductor can often be considered as the opposite of a capacitor

LC – Circuits and Energy +– LL CC S1S1 S2S2 At an arbitrary time t, where is the energy stored in this circuit? A)In the capacitor B)In the inductor C)Alternately in the capacitor or the inductor D)What energy?

LC - Circuits +– EE LL CC S1S1 S2S2 Switch S 1 is closed, then opened. At t = 0, switch S 2 is closed. What happens? I

LC – Circuits and Harmonic Oscillators These equations There are many correspondances between electrical and mechanical systems!

RLC circuits in Series II L C R S Do some algebra, and use

RLC circuits and Harmonic Oscillators L C R S A damped harmonic oscillator! Hence, the charge oscillations are the same as the motion of a damped harmonic oscillator.

Quiz A.A. B.B. C.C. D.D.

Electromagnetic Waves Electric Field Magnetic Field Direction of Motion

Using Maxwell’s Equations

Electromagnetic Waves These equations look like sin functions will solve them.

Electromagnetic Waves These equations imply The speed of light (in vacuum)