Question

A non-conducting sphere of radius R = 50 mm charged uniformly with surface density σ = 10.0 μC/m² rotates with an angular velocity ω = 70 rad/s about the axis passing through its centre. Find the magnetic induction at the centre of the sphere.

Answer 1

As only the outer surface of the sphere is charged, consider the element as a ring, as shown in the figure.

The equivalent current due to the ring element,

and magnetic induction due to this loop element at the centre of the sphere, O,

using above equation

Hence, the total magnetic induction due to the sphere at the centre, O,