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 inside the tube.

Step-by-step solution

The current i flows through the cross-section of the cylindrical tube between the inner radius a and outer radius b . For a point just inside the tube (in the hollow region), the radial distance r from the central axis is r a . Considering a circular Amperian loop of radius r a concentric with the axis of the tube, the current enclosed by this loop is zero, as the current flows only in the region a According to Ampere's circuital law: B d l = ₀ I_ enclosed Since I_ enclosed = 0 , we get: B(2 r) = 0 B = 0 Thus, the