Magnetic Fields

Because $\nabla \cdot {\bf B} = 0$, there are no magnetic monopoles (no magnetic point sources or sinks and no magnetic point charges) but just like an electric field we may define a magnetic dipole of moment ${\bf m}$ with a magnetic potential

$$F = {\mu_{0}\over 4\pi}{m\cos \theta\over r^{2}}.$$ (3.17)

The corresponding magnetic field, where the magnetic permeability is $\mu_{0} = 4\pi \times 10^{-7}$, is

$${\bf B} = -\nabla F,$$

with components

$$B_{r}= -{\partial F\over \partial r} = {\mu_{0}\over 4\pi}{... ...artial \theta} = {\mu_{0}\over 4\pi}{m\sin \theta\over r^{3}}.$$ (3.18)