Magnetic currents are fictitious, but they enable slot radiation to be solved by the same methods as electric currents on dipoles by using duality. Slot radiation could be calculated from the surface currents around it, but it is easier to use magnetic currents to replace the electric field in the slot. Magnetic currents along the long axis of slots in ground planes replace the electric fields across the slots by application of the equivalence theorem. Similarly, current loops can be replaced by magnetic dipole elements to calculate radiation.

We use the electric vector potential F with magnetic currents. The far-field magnetic field is proportional to the electric vector potential:

    (1)

We determine the magnitude of the electric field from Eq. (2)

it is perpendicular to H. The electric vector potential is found from a retarded volume integral over the magnetic current density M. Applying the radiation approximation, it is

    (3)

where ε is the permittivity ( ).. The dual of Eq. 4)

 is valid in both the near- and far-field regions.

The magnetic currents in a slot are perpendicular to the slot electric fields: M = E × ˆn, where ˆn is the normal to the plane with the slot. The filamentary currents of thin slots reduce Eq. (3) to a line integral, and magnetic current direction limits the direction of the electric vector potential and the magnetic field. Since the electric field

(far field) is orthogonal to the magnetic field, the electric field is in the same direction as the field across the slots. We use the direction of the electric field across the slots to estimate the polarization of the far field. As with filamentary electric currents, the far field is zero along the axis of the magnetic current.

The electric vector potential can also be used to derive the near field:

The magnetic field separates into near- and far-field terms in the electric vector potential; the electric field does not. We can determine the radiated fields directly in terms of the magnetic currents and avoid using the vector potential:

    (5)

    (6)

Equations (5) and (6) can be rearranged to find the dyadic Green’s functions for magnetic currents. These differ from the dyadic Green’s functions for electric currents by only constants.