Magnetic current

Magnetic current is, nominally, a current composed of fictitious moving magnetic monopoles. It has the dimensions of volts. The usual symbol for magnetic current is formula_1 which is analogous to formula_2 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 units of V/m2 (volts per square meter), is usually represented by the symbols formula_3 and formula_4. The superscripts indicate total and impressed magnetic current density. 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. It is possible to use both electric current densities and magnetic current densities in the same analysis.
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
Magnetic displacement current.
Magnetic displacement current or more properly the magnetic displacement current density is the familiar term It is one component of formula_6.
where
Electric vector potential.
The electric vector potential, F, is computed from the magnetic current density, formula_9, in the same way that the magnetic vector potential, A, is computed from the electric current density.
 F is used in the same way the magnetic vector potential for sources attributed to magnetic current. Examples of use include finite diameter wire antennas and transformers.
magnetic vector potential: formula_11
electric vector potential: formula_12
where F at point formula_13 and time formula_14 is calculated from magnetic currents at distant position formula_15 at an earlier time formula_16. The location formula_15 is a source point within volume Ω that contains the magnetic current distribution. The integration variable, formula_18, is a volume element around position formula_15. The earlier time formula_16 is called the "retarded time", and calculated as
Retarded time accounts for the accounts for the time required for electromagnetic effects to propagate from point formula_15 to point formula_13.
Phasor form.
When all the functions of time are sinusoids of the same frequency, the time domain equation can be replaced with a frequency domain equation. Retarded time is replaced with a phase term.
where formula_25 and formula_26 are phasor quantities and formula_1 is the wave number.
Magnetic frill generator.
A distribution of magnetic current, commonly called a magnetic frill generator, may be used to replace the driving source and feed line in the analysis of a finite diameter dipole antenna. The voltage source and feed line impedance are subsumed into the magnetic current density. In this case, the magnetic current density is concentrated in a two dimensional surface so the units of formula_4 are volts per meter.
The inner radius of the frill is the same as the radius of the dipole. The outer radius is chosen so that
where
The equation is the same as the equation for the impedance of a coaxial cable. However, a coaxial cable feed line is not assumed and not required.
The amplitude of the magnetic current density phasor is given by:
where 