I'm trying to read through a lab manual for showing the inverse square law of magnetism by Gauss' Method.
The following diagram is given
where M is the magnetic moment of the test magnet. $H_0$ is the horizontal component of earth's magnetic field.
It introduces this set of equations for the "Inverse $n^{th}$ power law":
Magnetic field at position A, $$ H_A = \frac{nM}{d^{n+1}}\frac{\mu_0}{4\pi}$$
Magnetic field at position B, $$ H_B = \frac{M}{d^{n+1}}\frac{\mu_0}{4\pi}$$
From where do these set of equations come from? Alternatively: Is there a clear resource on Gauss' method for this experiment?