A long cylindrical tube with inner and outer radii a and b carries a current i that is distributed uniformly across its cross section. Determine the magnitude of the magnetic field at a location just outside the tube.

Step-by-step solution

Using Ampere's circuital law: B d l = ₀ I_ enclosed For a point just outside the cylindrical tube, the radial distance from the axis is r = b . Considering a circular Amperian loop of radius r = b coaxial with the tube, the total current enclosed by this loop is the entire current i carried by the tube. B (2 b) = ₀ i B = ₀ i 2 b