Magnetic current

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Magnetic current is, nominally, a current composed of moving magnetic monopoles. It has the unit volt. The usual symbol for magnetic current is ${\displaystyle k}$, which is analogous to ${\displaystyle i}$ for electric current. Magnetic currents produce an electric field analogously to the production of a magnetic field by electric currents. Magnetic current density, which has the unit V/m² (volt per square meter), is usually represented by the symbols ${\displaystyle {\mathfrak {M}}^{\text{t}}}$ and ${\displaystyle {\mathfrak {M}}^{\text{i}}}$.^[a] The superscripts indicate total and impressed magnetic current density.^[1] The impressed currents are the energy sources. In many useful cases, a distribution of electric charge can be mathematically replaced by an equivalent distribution of magnetic current. This artifice can be used to simplify some electromagnetic field problems.^[b][c] It is possible to use both electric current densities and magnetic current densities in the same analysis.^[4]: 138

The direction of the electric field produced by magnetic currents is determined by the left-hand rule (opposite direction as determined by the right-hand rule) as evidenced by the negative sign in the equation^[1] $${\displaystyle \nabla \times {\mathcal {E}}=-{\mathfrak {M}}^{\text{t}}.}$$

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