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?
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1$\begingroup$ Show us your derivation, or a source which derives it and why you distrust one or the other solution. $\endgroup$– planetmakerCommented Oct 5, 2023 at 6:12
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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.
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$\begingroup$ Thank you @ProfRob. However with m = (2\mu_0)}*R^3*g_1^0 is it not B_r = 2(R/3)^3* g_1^0 *cos(theta) which is the same as I wrote ? $\endgroup$ Commented Oct 6, 2023 at 15:57
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$\begingroup$ I have no idea what your comment means. @LunthangPeter $\endgroup$– ProfRobCommented Oct 6, 2023 at 21:11