Speaking of the Lorentz force, the minus sign comes in on the equivalent force on a monopole like so:

F = g(H - v x D) (using the traditional 'g' to be the magnetic charge), or, putting it in force density terms:

f = rho_g(H - J_g x D), where J_g is the monopole current density.

And this shows something interesting. Many physicists prefer to think of E and B as the "fundamental fields", because they give the force on a particle directly. Well, with monopoles, it would be just the opposite, with D and H giving the force. I prefer to think of E and H, and D and B as the "pairs that go together".

And this shows something interesting (at least to me -- duality relations always fascinated me to no end). The force on an electric charge goes as E and B. This means that the force on charges is reduced by a medium with a higher permittivity, but the magnetic force between electric currents is *increased* by higher permeability. Surround your wires with iron, and the magnetic forces are increased.

So in an electric charge-only universe, there is tendency to think of epsilon and mu as sort of working backwards to each other, and that's the (E, B) vs (D, H) pairing POV.

However consider monopoles, and you see that flips around. The magnetic force between monopoles would be decreased by higher mu, but the electric force between monopole currents would be increased by a dielectric material.

The Duality picture exposes a lot of cut symmetries. For example, the voltage of the one is the current of the other. A volt is an electric potential (or EMF), energy per electric-charge, but it is also magnetic current, magnetic charge per time. And likewise an amp, electric-charge per time is also energy per magnetic-charge.

So if want the equivalent magnetic unit, you just sort of flip volts and amps and coulombs and webers. What would the unit of "magnetic capacitance" be? Well, capacitance is charge per unit voltage. In electric terms, that's a coulomb per volt (which we call a Farad).

Let's flip it to get the magnetic equivalent. That's a weber per magnetic voltage, which is a weber per amp, or a Henry, the unit of electric current inductance!

And so you then immediately realize that a Farad is thus the unit of magnetic current inductance. (but note there is a subtle difference between these. Capacitors make divergent dipoles, while coils make solenoidal ones -- the units are the same, but they are different. A coil of magnetic monpole current would make a solenoidal E-field, and a monopole capacitor would make a divergent H field).

Resistance and conductance would be flipped exactly. Magnetic current resistance is voltage per current, which is an amp per volt for monopoles, or a mho. Thus magnetic conductance is in ohms.

I always thought of that as just slick and it fascinates me to no end.

The meaning of volts, amps, and all electrical units "rotates and flips" as you change your basis in the charge/field space of Duality.

-Richard