I was wondering about the differences between electricity and magnetism in the context of Maxwell's equations. When I thought over it, I came to the conclusion that the only difference between the two is that magnetic monopoles do not exist. Is this right?
Next one. Now I searched for the equations with magnetic monopoles and found them at Wikipedia. They seem quite symmetrical (except the constants of course), except two major differences:
It is $\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}} {\partial t} - \mu_0\mathbf{j}_{\mathrm m}$, but $\nabla \times \mathbf{B} = \mu_0 \epsilon_0 \frac{\partial \mathbf{E}} {\partial t} + \mu_0 \mathbf{j}_{\mathrm e}$. This means that the induced "magnetic emf" (if I may call it that) is produced by changing electric fields and currents in the exact opposite sense (I mean direction) to the counterpart phenomenon of Electromagnetic Induction. Why so?? Is there a lenz law for "magnetic emf" induction also??
Also, the lorentz force on magnetic charges $\mathbf {F}={}q_\mathrm m (\mathbf {B} - {\mathbf v} \times \frac {\mathbf {E}} {c^2})$. Why this minus sign in the force on magnetic charges that does not appear in the lorentz force on electric charges.