Electricity and Magnetism Physics 208 Dr. Tatiana Erukhimova Lecture 29

Current carrying wires 1820 Hans Christian Oersted Hans Christian Ørsted

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.

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)

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

Field of a Current Carrying Loop x (along x)

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?

Exercise 5

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

Induced EMF and Inductance 1830s Michael Faraday Joseph Henry