Verify the Gauss’ law for magnetic field

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magnetism

#1

Verify the Gauss’ law for magnetic field of a point dipole of dipole moment M at the origin for the surface which is a sphere of radius R.


#2

Let us draw the figure for given situation,


According to the question,
Magnetic moment of dipole at origin O is

Let P be a point at distance r from O and OP makes an angle 0 with .Z-axis. Component of M along OP = M cos 0. Now, the magnetic field induction at P due to dipole of moment M cos 0 is
B = ${ µ }_{ 0 }$ / 4 $\pi$ . 2M cosθ / ${{r}^{3}}$ r^
From the diagram, r is the radius of sphere with centre at O lying in FZ-plane. Take an elementary area dS of the surface at P. Then,