1. Electricity and Magnetism
Physics 208
Dr. Tatiana Erukhimova
Lecture 30

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

4. 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. Field of a Current Carrying Loopx
(along x)

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

7. 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.

8. Problem 1
Consider two infinitely long, parallel wires a distance d apart. Find the force between them if they both carry equal currents, i
One Ampere is that current which, when flowing in each of two very long, straight, parallel wires, one meter apart, causes each wire to feel a force of attraction of 2x10-7 Newtons per unit length.
Coulomb is amount of charge which passes a surface in 1 sec if current through it is 1 A

9. 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?

10. 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.

11. Exercise 5

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