2. Problem 3 An infinitely long wire has 5 amps flowing in it. A rectangular loop of wire, oriented as shown in the plane of the paper, has 4 amps in it. What is the force exerted on the loop by the long wire?

3. Consider the coaxial cable shown below. This represents an infinitely long cylindrical conductor carrying a current i spread uniformly over its cross section and a cylindrical conducting shell around it with a current i flowing in the opposite direction. The second i is uniformly spread over the cross section of the shell. Find magnetic field everywhere. c b ai

4. Induced EMF and Inductance 1830s Michael Faraday Joseph Henry

5. Faraday’s Law of Induction The induced EMF in a closed loop equals the negative of the time rate of change of magnetic flux through the loop

6. There can be EMF produced in a number of ways: A time varying magnetic field An area whose size is varying A time varying angle between and Any combination of the above

8. R From Faraday’s law: a time varying flux through a circuit will induce an EMF in the circuit. If the circuit consists only of a loop of wire with one resistor, with resistance R, a current Which way? Lenz’s Law: if a current is induced by some change, the direction of the current is such that it opposes the change.

10. The Moving Circuit There is a uniform magnetic field out of the board. A rectangular circuit is pulled at a constant speed to the right. What current flows in the circuit if the total resistance of the circuit is R?

11. The magnetic field between the poles of the electromagnet is uniform, but its magnitude is increasing at the rate of 0.020 T/s. The area of the conducting loop in the field is 120 cm 2, and the total circuit resistance, including the meter and the resistor, is 5.0 Ώ. Find the induced EMF and the induced current in the circuit.

12. Problem 3 A rod with resistance R 1 slides without friction on two resistance-free tracks which are connected by a resistor, R 2. A wire, carrying a current i, is parallel to the tracks, in the same plane. Ignoring the self-inductance of the circuit, calculate the current that flows through R 2 as a function of the velocity of the rod.

13. Exercise 4 An infinitely long wire has a current given by where i 0 and ω are constants. A regular loop of wire is placed near the wire. If the rectangular loop has resistance R, what current will flow in it?

14. A Simple Generator

15. Induced EMF and Inductance 1830s Michael Faraday Joseph Henry M is mutual inductance