Classical Electrodynamics · Problem 5.14

Maxwell Equations, Macroscopic Electromagnetism, Conservation Laws — John David Jackson

Physics — E&M · permeable-cylinder-uniform-field

Problem

A long, hollow, right circular cylinder of inner (outer) radius

a

(

b

), and of relative permeability

\mu_r

, is placed in a region of initially uniform magnetic-flux density

\mathbf{B}_0

at right angles to the field. Find the flux density at all points in space, and sketch the logarithm of the ratio of the magnitudes of

\mathbf{B}

on the cylinder axis to

\mathbf{B}_0

as a function of

\log_{10}\mu_r

for

a^2/b^2 = 0.5, 0.1

. Neglect end effects.