(a) Show by applying Ampere's circuital law that the magnetic field associated with a long straight, current-carrying wire is given by Bφ = µ0I/(2πr), where the subscript φ denotes the φ-component in the circular cylindrical coordinate system,µ0 is the free-space permeability, I is the current carried by the wire, and r is the radius from the current carrying wire. What is the net force on the wire due to the interaction of the B-field (produced by the current I) and the current I?
(b) A magnetic force exists between two adjacent, parallel, current-carrying wires. Let I1 and I2 be the currents carried by the wires and r the separation between them. Use the result of part (a) to find the force between the wires. Discuss the nature of the force when the wires carry currents in the same direction, and in opposite directions.