Magnetic Monopole (Magnetic Charge)

An electric charge produces a Coulomb electric field:
E = dq_e r/r³

A current element produces a Biot-Savart magnetic field
B = i dl×r /r³

From what I understand, magnetic charges are inserted for the sake of making Maxwell's equations symmetric.

A magnetic charge is meant to produce a Coulomb magnetic field:
B = dq_m r /r³

So if magnetic monopoles are allowed, shouldn't there also be an analogous version of the electric current element that produces a Biot-Savart electric field?

E = i_e dl×r /r³

What would such a thing be called? Where would I find information about these kinds of objects?