Magnetic fields?

Question

Hi,

There is a cable that consists of a solid inner conductor with radius R1, surrounded by a hollow, very thin outer conductor with radius R2. The two carry equal currents I, but in opposite directions. The current density is uniformly distributed over each conductor.

a) Find expressions for the 3 magnetic fields: within the inner conductor, in the space between the conductors, and the outside of the outer conductor.

b) Graph B versus r from r = 0 to r = 2(R2) if R1 = (1/3)(R2)


I am thinking of using the formula of B = v x (Uo)/(4pi) x q/r^2 x r(hat). Am I on the right track. Any help would be appreciated!


Thanks!

Answer 1

for the inside conductor, inside the conductor
∫B.dl=u0i (Ampere's law)

B=u0ri/2π(R1)^2 where r is the distance from the center of the conductor to the edge of the inner conductore.

for the zone between conductors

B=u0I/2πr

for the area outside the conductors (inner and outer), B=0