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

2. Current carrying wires
1820 Hans Christian Oersted
Hans Christian Ørsted

3. 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)

5. Ampere’s Law
The field produced by an infinite wire

6. 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.

7. 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?

8. 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.

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

10. 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

11. 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

13. 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.