Show that the magnetic dipole moment of a uniformly magnetiz

Show that the magnetic dipole moment of a uniformly magnetized scheme is m = 4/2 pi r^3 H where H is magnetization

Solution

A uniformly magnetized and conducting sphere of radius and total magnetic moment m

rotates about its magnetization axis with angular speed

Place the sphere at the origin and align the spin axis with the z axis. Because the total magnetic

moment m is the spatial integral of the magnetization M and the sphere is uniformly magnetized, so that

m= M( x)dx= MV =M (4/3) Pi R³