Magnetic Field at the center of a sphere magnet

[hansbahia]

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

j_M(θ)=Msin(θ)

dI=j_M(θ)adθ

circular loop

r_{loop}=asin(θ)

The Attempt at a Solution

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

instead of

R^3=(r_{loop}^2+z^2)

for the denominator?

 

[TSny]

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

instead of

R^3=(r_{loop}^2+z^2)

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?