Electricity and Magnetism Physics 208 Dr. Tatiana Erukhimova Lectures 31-32

Induced EMF and Inductance 1830s Michael Faraday Joseph Henry

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

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

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 R 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.

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?

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 cm2, 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.

Problem 3 A rod with resistance R1 slides without friction on two resistance-free tracks which are connected by a resistor, R2. 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 R2 as a function of the velocity of the rod.

Exercise 4 An infinitely long wire has a current given by where i0 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?

A Simple Generator

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