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 (Also called Ampere’s principle) is called permeability of free space

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 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.

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?

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

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.