A long, thin, hollow cylindrical tube of radius r carries a current i along its length. Calculate the magnitude of the magnetic field at a distance r/2 from the surface, outside the tube.

Step-by-step solution

Let the distance of the point from the axis of the cylinder be R . Since the point is at a distance r/2 from the surface outside the tube, we have R = r + r 2 = 3r 2 . By Ampere's circuital law, the magnetic field outside a long cylindrical tube carrying current i is given by: B d l = ₀ i B(2 R) = ₀ i B = ₀ i 2 R Substituting R = 3r 2 : B = ₀ i 2 ( 3r 2 ) = ₀ i 3 r