An infinitely long circular cylinder carries a uniform magnetization Mparallel to its axis. Find the magnetic field (due toM) inside and outside the cylinder.

Short Answer

Expert verified

The value of magnetic field inside and outside the cylinder isBins=μ0Mz^ andBout=0 .

Step by step solution

01

Write the given data from the question.

Consideran infinitely long circular cylinder carries a uniform magnetizationM parallel to its axis.

02

Determine the formula of magnetic field inside the cylinder.

Write the formula of magnetic field inside the cylinder.

B=μ0K …… (1)

Here,μ0 is permeability andK is surface current.

03

Determine the value of magnetic field inside and outside the cylinder.

Thereisnovolumeboundcurrentsincethecylinder'smagnetizationishomogeneous;instead,thereissurfaceboundcurrent.

Determine the surface bound current.

Kb=M×n=Mz^×s^=Mϕ

This is the field of an infinite solenoid with surface current,nI=K=M therefore the outside field is and the inner field is:Bout=0

Determine the magnetic field inside the cylinder.

SubstituteMz^ forK into equation (1).

Bins=μ0Mz^=μ0M

Therefore, the value of magnetic field inside and outside the cylinder is Bins=μ0Mz^ and Bout=0.

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Figure 6.30

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