Announcements

1. Announcements Change of plans for today: Demos on light and selected review for today

2. Faraday’s Law 5 T 10  3 m/s 2 m 10 m What is the current induced in this circuit? • 30A • 3 A • 10A D) 6A

3. Faraday’s Law 5 T 10  3 m/s 2 m 10 m 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.

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

5. 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: 2p (2R)E =-p(R2) dB/dt, so E= (-(R2) /4) dB/dt=0.0045 V/m

6. 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.

7. 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? Quiz

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

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

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

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

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

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

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

15. Quiz A. B. C. D.

16. Electric Field Magnetic Field Direction of Motion Electromagnetic Waves

17. Using Maxwell’s Equations

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

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