1. Electricity and Magnetism
Physics 208
Dr. Tatiana Erukhimova
Lecture 29

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

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

4. 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.

5. 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)

6. 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

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

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. 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. Exercise 5

11. Consider the coaxial cable shown below
Consider the coaxial cable shown below. This represents an infinitely long cylindrical conductor carrying a current i spread uniformly over its cross section and a cylindrical conducting shell around it with a current i flowing in the opposite direction. The second i is uniformly spread over the cross section of the shell. Find magnetic field everywhere. b a i c

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