Consider an infinite straight coaxial cable consisting of a

Consider an infinite straight coaxial cable consisting of a cylindrical wire, surrounded by a layer of insulation, which is surrounded by a conducting sheath (like a pipe), which is surrounded by another insulationg layer. Assume that the radius of the inner conductor is R, the inner radius of the outer sheath is 2R and that the sheath has a negligible thickness. Assume that the inner wire carries a current of I toward the viewer, and the sheath carries the same magnitude of current in the opposite direction. Caluculate the magnetic field inside the inner wire, between the wire and the sheath, and outside the cable, and present your results by drawing a quantitatively accurate graph of B(r) for 0<=r<=3R.

Solution

1) at 0<r<R (in side the inner codtcor)

B = mue*I*r/(2*pi*R^2)

at r = R (on the surface of inner consuctor)

B = mue*I/(2*pi*R)

2) at R<r<2*R ( in between inner condctor and sheeath)

B = mue*I/(2*pi*r)

3) at r>2*R (out side the sheath)

B = mue*(I-I)/2*pi*r

= 0