1. PHY 2049: Physics II Tutoring Center is open in room NPB 1100, M-F 10:00AM -3:00PM. It is free. Hopefully all webassign problems have been solved. Please see me immediately after the class if there is still an issue.

2. PHY 2049: Physics II About bicycle riding: If some one shows you a trick, it means that, It is possible to do that trick The person who showed you, can do the trick. It does not mean that you can do the trick. Try it a lot of times and you can too.

3. PHY 2049: Physics II Recall: Faraday’s law Lenz’ law: the kickback

4. PHY 2049: Physics II Recall more Inductors and inductance Emf induced in a coil when the current changes Solenoids L = μ 0 n 2 lA RL circuits I = (1-e -t/τ )V/Rτ = L/R Energy in a magnetic field U = ½ Li 2, u = B 2 /2μ o In a coaxial cable the surface is most stressed.

5. PHY 2049: Physics II Mutual induction E 2 = -M 21 di 1 /dt M 21 = M 12 Coil in a coil

6. PHY 2049: Physics II Three circuit elements: CapacitorV = Q/C ResistorV = IRI = dQ/dt InductorV =- LdI/dt A general circuit is a combination of these elements. The analysis is a bit subtle.

7. PHY 2049: Physics II

8. a.Long after the switch is closed In each case the current through R is shorted by the inductor. The inductor carries all of the current. b. Switch is opened. The equivalent resistances are (1) R (2) 2R and (3) R/2. Hence by current, the ranking is 3 1 2. c. Long after the switch is opened, there is no current anywhere.

9. PHY 2049: Physics II

10. Problem 32: The area is v 2 t 2, you can convince yourself that the two sides of the triangle are each 2vt/√2. Area A = ½ (2vt/√2) 2 At t= 3 s. Flux = BA = 0.35x 5.2 2 x3 2 = 85.2 Wb Emf around: 56.8 V Emf = 18.93t., n = 1

11. PHY 2049: Physics II L 1 = 30 mH L 2 = 50 mH L 3 = 20 mH L 4 = 15 mH

12. PHY 2049: Physics II L 1 = 30 mH L 2 = 50 mH L 3 = 20 mH L 4 = 15 mH L 23 = 14.3 L eq = 30 +15 + 14.3 = 59.3 mH

13. PHY 2049: Physics II

14. E =Ldi/dt i = Et/L t = iL/E = 1.5s

15. PHY 2049: Physics II LC oscillations Ld 2 Q/dt 2 +Q/C = = For a spring Md 2 x/dt 2 +kx =0 Solution is x = A cosωt ω = √(k/m) Here ω = 1/ √(LC) When there is a natural frequency, there is violent response => resonance Quantitymechelectronic MassmL Spring k1/C PositionxQ

16. PHY 2049: Physics II Inductors and inductance Currents are slowed down by Faraday’s law Eddy currents More later