2. 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.

3. Generality of Faraday’s Law Faraday’s law applies when moving a wire in a magnetic field However, changing magnetic fields also produce an EMF. Changing magnetic fields must produce electric fields! What is the nature of the force? It is not a magnetic force because the charges are not necessarily moving

4. Faraday’s Law and Electric Fields q

5. . 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=0.0045 V/m

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

8. 3 k  9 k  3 k  What is the combined resistance of the mess at right? A)1.5 k  B)12 k  C)14 k  D)21 k  6 k  2 k 

9. +–+–  9 V 5   1.5 V 3  I1 I1 I3 I3 I2 I2 What is the conservation of current law associated with the junction on the right? A)I 1 + I 2 = I 3 B) I 1 + I 3 = I 2 C) I 2 + I 3 = I 1 D)I 1 + I 2 + I 3 = 0 What is the voltage loop rule you get applied to the upper loop? A)9 + 5I 1 + 3I 2 = 0 B)9 + 5I 1 – 3I 2 = 0 C)9 – 5I 1 + 3I 2 = 0 D)9 – 5I 1 – 3I 2 = 0 I 1 + I 3 = I 2 1.5 – 3I 2 = 0 9 – 5I 1 – 3I 2 = 0 I 2 = 1.5/3 = 0.5 A I 1 = (9 – 3I 2 )/5 = 1.5 A I 3 = I 2 – I 1 = 0.5 – 1.5 = – 1 A A Multiloop Circuit

10. +–+–  9 V 5   9 V Odd Circuit What is the current through the resistor? A) 3.6 A B) 1.8A C) 90 A D) 0 A

11. Four circuits have the form shown in the diagram. The capacitor is initially uncharged and the switch S is open. The values of the emf, resistance R, and the capacitance C for each of the circuits are circuit 1: 18 V, R = 3, C = 1 µF circuit 2: 18 V, R = 6, C = 9 µF circuit 3: 12 V, R = 1, C = 7 µF circuit 4: 10 V, R = 5, C = 7 µF Which circuit has the largest current right after the switch is closed? Which circuit takes the longest time to charge the capacitor to ½ its final charge? Which circuit takes the least amount of time to charge the capacitor to ½ its final charge?

13. Torque on a Loop What is the torque on the wire? A)4  10 -2 N  mD)  10 -4 N  m B)  10 -2 N  m C)4  10 -4 N  m B = 1 T 2 cm Which direction does the torque twist the loop? A)Right towards, left away B)Right away, left towards C)Top towards, bottom away D)Bottom towards, top away I = 1A

14. Quiz: Ampere’s Law Which of the loops has the largest and smallest integrals of the magnetic field around the loops drawn? A)X > Y > ZC) Y > Z > X B)X > Z > YD) Y > X > Z 2 A 3 A 1 A Consider three wires with current flowing in/out as shown X Y Z Consider three different loops surrounding the wires

15. Quiz A)Remains the same B)Reverses C)Changes in magnitude but not direction D)Changes to some other direction