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

Hint: Use Gauss' law.
Step 1: Let us draw the figure for the given situation.
We have to prove that BdS=0. This is called Gauss's law in magnetization.
According to the question, the magnetic moment of the dipole at origin O is;
M = Mk^
Let P be a point at distance r from O and OP makes an angle θ with the z-axis.
Component of M along OP= M cos θ.
Now, the magnetic field induction at P due to the dipole of moment Mcosθ is:
B=μ04π2M cos θr3r^
From the diagram, r is the radius of the sphere with center at O lying in the yz-plane. Take an elementary area dS of the surface at P. Then,