Faradays Law 10 5 T 3 ms 2

Faraday’s Law 10 5 T 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.

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. What is the nature of the force? It is not a magnetic force because the charges are not necessarily moving Changing magnetic fields must produce electric fields!

Faraday’s Law and Electric Fields q

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 2 R from the cylinder axis is: Using Faraday’s law: 2 (2 R)E =- (R 2) d. B/dt, so E= (-(R 2) /4) d. B/dt=0. 0045 V/m

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

What is the combined resistance of the mess at right? A) 1. 5 k B) 12 k C) 14 k D) 21 k 9 k 3 k 6 k 2 k 3 k

A Multiloop Circuit I 1 + I 3 = I 2 1. 5 – 3 I 2 = 0 9 – 5 I 1 – 3 I 2 = 0 I 2 = 1. 5/3 = 0. 5 A I 1 – + 9 V 5 I 2 3 I 3 1. 5 V – + What is the voltage loop rule What is the conservation of you get applied to the upper current law associated with I 1 = (9 – 3 I 2)/5 = 1. 5 A loop? the junction on the right? A) A) 9 + 5 I I 1 + I 21 = I + 3 I 3 2 = 0 I 3 = I 2 – I 1 = 0. 5 – 1. 5 = – 1 A B) B) 9 + 5 I I 1 + I 1 3 = I – 3 I 22 = 0 C) C) 9 – 5 I I 2 + I 1 3 = I + 3 I 12 = 0 D) D) 9 – 5 I I 1 + I 21 + I – 3 I 3 = 0 2 = 0

Odd Circuit What is the current through the resistor? A) 3. 6 A B) 1. 8 A C) 90 A D) 0 A – + 9 V 5 9 V – +

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?

Torque on a Loop B = 1 T 2 cm I = 1 A What is the torque on the wire? A) 4 10 -2 N m D) 10 -4 N m B) 10 -2 N m C) 4 10 -4 N m 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

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

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