Magnetic Monopole - Maxwell's Equations

Maxwell's Equations

Maxwell's equations of electromagnetism relate the electric and magnetic fields to each other and to the motions of electric charges. The standard equations provide for electric charges, but they posit no magnetic charges. Except for this difference, the equations are symmetric under the interchange of the electric and magnetic fields. In fact, symmetric Maxwell's equations can be written when all charges (and hence electric currents) are zero, and this is how the electromagnetic wave equation is derived.

Fully symmetric Maxwell's equations can also be written if one allows for the possibility of "magnetic charges" analogous to electric charges. With the inclusion of a variable for the density of these magnetic charges, say ρ_m, there will also be a "magnetic current density" variable in the equations, j_m.

If magnetic charges do not exist – or if they do exist but are not present in a region of space – then the new terms in Maxwell's equations are all zero, and the extended equations reduce to the conventional equations of electromagnetism such as ∇⋅B = 0 (where ∇⋅ is divergence and B is the magnetic B field).

Top: E field due to an electric dipole moment d. Bottom left: B field due to a mathematical magnetic dipole m formed by two magnetic monopoles. Bottom right: B field due to a natural magnetic dipole moment m found in ordinary matter (not from monopoles). The E fields and B fields due to electric charges (black/white) and magnetic poles (red/blue).