Question

9-2 (a) Find the distribution of magnetization currents corresponding to a uniformly magnetized sphere with magnetization M. According to Eq. (9-63) the magnetic induction B is uniform inside such a sphere. (b) Can you use this information to design a current winding that will produce a uniform magnetic field in a spherical region of space?

Answer 1

We know for magnetic field volume current: T_l = 8 times m surface current: - u_f = m times n for the spherical of Jell let M - m H J_l r times m = 0 [m = constant magnetation] therefore now, for a sphere n = r there k_f = m k times r In the spherical polar co-ordinate Now r cos theta sin theta i + sin theta sin theta j + cos theta n x times r = cos theta sin theta (x times i) + sin phi sin theta (x times j) + cos theta (x times x) \r\n = cos theta sin theta j + sin theta sin theta (- j) = -sin theta sin theta j + cos theta sin theta j = phi sin theta [phi = -sin theta + cos theta j] u_f = m x times r