Electricity and Magnetism Physics 208 Dr. Tatiana Erukhimova Lectures 29, 30

Current carrying wires 1820 Hans Christian Oersted Hans Christian Ørsted

Biot-Savart Law Infinitesimally small element of a current carrying wire produces an infinitesimally small magnetic field is called permeability of free space (Also called Ampere’s principle)

Ampere’s Law The field produced by an infinite wire

Problem 6 An infinitely long, hollow cylindrical wire has inner radius a and outer radius b. A current i is uniformly distributed over its cross-section. Find the magnetic field everywhere.

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?

Problem 4 Consider a very long (essentially infinite), tightly wound coil with n turns per unit length. This is called a solenoid. Assume that the lines of B are parallel to the axis of the solenoid and non-zero only inside the coil and very far away. Also assume that B is constant inside. Find B inside the solenoid if there is a current i flowing through it.

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.