91Ó°ÊÓ

Consideran infinitely long circular cylinder carries a uniform magnetization$\mathrm{M}$ parallel to its axis.

Write the formula of magnetic field inside the cylinder.

$\stackrel{\mathbf{→}}{\mathbf{B}}\mathbf{=}{\mathit{μ}}_0\mathbf{K}$ …… (1)

Here,${\mathit{μ}}_0$ is permeability and$\mathbf{K}$ is surface current.

Thereisnovolumeboundcurrentsincethecylinder'smagnetizationishomogeneous;instead,thereissurfaceboundcurrent.

Determine the surface bound current.

$\begin{array}{c}{\stackrel{→}{K}}_b=\stackrel{→}{M}×\stackrel{→}{n}\\ =M\widehat{z}×\widehat{s}\\ =M\mathrm{ϕ}\end{array}$

This is the field of an infinite solenoid with surface current,$\mathrm{nI}=\mathrm{K}=\mathrm{M}$ therefore the outside field is and the inner field is:${\stackrel{→}{B}}_{out}=0$

Determine the magnetic field inside the cylinder.

Substitute$M\widehat{z}$ for$K$ into equation (1).

$\begin{array}{c}{\stackrel{→}{B}}_{ins}={\mathrm{μ}}_{0}M\widehat{z}\\ ={\mathrm{μ}}_0\stackrel{→}{M}\end{array}$

Therefore, the value of magnetic field inside and outside the cylinder is ${\stackrel{→}{B}}_{ins}={\mathrm{μ}}_{0}M\widehat{z}$ and ${\stackrel{→}{B}}_{out}=0$.