# Deriving Electromagnetic Theory

• spaghetti3451
In summary, magnetic monopoles postulate the existence of charges that have a magnetic field only and that interact with electric fields. Duality allows for the replacement of electric fields with magnetic fields in differential equations, which can simplify calculations.f

#### spaghetti3451

Hi,

I am trying to re-derive, or should I say modify, the existing theory of classical electromagnetism by postulating the existence of magnetic monopoles. Where should I begin?

This is a subject that is covered in many engineering books. In the end, it makes Maxwell's Equations symmetrical. The divergence of the magnetic flux density is the magnetic charge density, just like how the divergence of the electric flux density is the electric charge density. There will also be magnetic currents as well. You can change between the electric and magnetic fields for a given equation in such a system by making use of duality. I do not have my references on hand but basically it allows you to replace the electric field in an equation with the magnetic field and something similar with the permittivity, permeability, charges and currents.

Allowing for magnetic currents is often done in computations because the behavior of magnetic currents is like the "dual" of the electric currents. For example, I can excite the same electromagnetic wave from a given electric current by a magnetic current. The magnetic and electric currents will be related to each other along the lines of the curl operator. So a linear dipole electric current is equivalent to a loop of magnetic current and vice-versa. This can allow us to more easily express the excitations of a field using magnetic currents.

Weng Cho Chew's "Waves and Fields in Inhomogeneous Media" discusses duality but many electrical engineering texts will probably have it (more so if they deal with computational methods or antennas since magnetic currents often arise in those subjects).

It was also discussed in the edition of Halliday and Resnick's first-year physics textbook that I used nearly forty years ago. I don't know if the current editions still do this.

Thanks! I'll use the books and if I have any further questions, I hope you won't mind answering them. :-)

It might be useful to know, if you are using the Maxwell-Herz equations in differential form, to sign the magnetic current using the convention

$$-\nabla \times E - \frac{\partial B}{\partial t} = J_{magnetic}$$