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**[SOLVED] Griffiths 5.58**

**1. Homework Statement**

A uniformly charged solid sphere of radius R carries a total charge Q, and is set spinning with angular velocity \omega.

What is the magnetic dipole moment of the sphere.

**2. Homework Equations**

**3. The Attempt at a Solution**

The magnetic dipole moment of a disk is

[tex](1/4) r^4 \sigma \pi \omega[/tex]

Why does

[tex]\int_0^{\pi} (Rd\theta) ((1/4) R^4 \sin^4 \theta \sigma \pi \omega)[/tex]

with [itex]\sigma[/itex] replaced by [itex]3Q/(4 \pi R^3)[/itex] not give the correct answer?