Maxwell Equations, Macroscopic Electromagnetism, Conservation Laws — John David Jackson
Physics — E&M · loop-in-spherical-iron-cavity
Problem
A circular loop of wire of radius a and negligible thickness carries a current I. The loop is centered in a spherical cavity of radius b>a in a large block of soft iron. Assume that the relative permeability of the iron is effectively infinite and that of the medium in the cavity, unity.
(a) In the approximation of b≫a, show that the magnetic field at the center of the loop is augmented by a factor (1+a3/2b3) by the presence of the iron.
(b) What is the radius of the ``image'' current loop (carrying the same current) that simulates the effect of the iron for r<b?