Magnetic Field at the center of a sphere magnet

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Homework Statement


A sphere magnet of radius a has permanent uniform magnetization, z-axis. So we were trying to find the magnetic field at the center of the magnet in class.

Homework Equations


[itex]j_M(θ)=Msin(θ)[/itex]

[itex]dI=j_M(θ)adθ[/itex]

circular loop

[itex]r_{loop}=asin(θ)[/itex]


The Attempt at a Solution



When using Biot-Savart equation for magnetic field of a ring why do you use*
[itex]R^3=(a^2+z^2)[/itex]

instead of

[itex]R^3=(r_{loop}^2+z^2)[/itex]

for the denominator????
 
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Answers and Replies

  • #2
TSny
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When using Biot-Savart equation for magnetic field of a ring why do you use*
[itex]R^3=(a^2+z^2)[/itex]

instead of

[itex]R^3=(r_{loop}^2+z^2)[/itex]

for the denominator????

Did you mean to write R2 instead of R3?

Can you show that the effective current due to the magnetization is zero everywhere except at the surface of the sphere?
 

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