# Is the magnetic permeability (mu_0) necessary in the expression for planetary magnetic field?

To numerically analyse the Lorentz effect due to the magnetic field, say, radial component on a charge particles which of the expression would be correct, $$\{ B_r = \frac{2R}{r^3} g_1^0 \cos(\theta) \}$$ or $$\{ B_r = \mu_0 \frac{2R}{r^3} g_1^0 \cos(\theta) \}$$ ? Assuming there are no other particles and the particle is in the gravitational and magnetic field of the planet?

• Show us your derivation, or a source which derives it and why you distrust one or the other solution. Commented Oct 5, 2023 at 6:12

It entirely depends what system of units you are working in. $$\mu_0 \simeq 4\pi\times 10^{-7}$$ in S.I. units.
However, in Gaussian units, $$\mu_0=1$$ and so it isn't included.
In Gaussian units, the radial component of a magnetic dipole field is $$B_r =\frac{2m}{r^3}\cos\theta$$ measured in Gauss, where $$m$$ is a magnetic dipole moment.
In SI units, the same dipole has a radial field $$B_r = \frac{2\mu_0 m}{4\pi r^3}\cos\theta$$ in Tesla.