Faraday's Law of Induction and Electric Fields

1. 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.

2. 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!

3. Faraday’s Law and Electric Fields q

4. 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

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

7. 6 k 2 k • What is the combined resistance of the mess at right? • 1.5 k • 12 k • 14 k • 21 k 9 k 3 k 3 k 3 k 3 k

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

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

10. 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 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?

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

13. Consider three wires with current flowing in/out as shown • Consider three different loops surrounding the wires X 2 A Y 3 A Z 1 A 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 > Z C) Y > Z > X B) X > Z > Y D) Y > X > Z

14. Quiz • Remains the same • Reverses • Changes in magnitude but not direction • Changes to some other direction