Mawell equations with monopoles

[nos]

Hi all,

Suppose magnetic monopoles exist, how would the maxwell equations be solved?
Because the divergence of B is no longer zero, we can not use the vector potential, can we? Do you just solve for the electric and manetic field for electric charges and magnetic charges seperately and then add them together to get the total fields? How would one approach this?

I guess the answer would be:
E= electric field generated by magnetic charge + electric field generated by electric charge
B= magnetic field generated by electric charge + magnetic field generated by magnetic charge.
This would then be a more general solution. You can still get the old fields by setting the magnetic charge equal to zero.
I would like to do this a an exercise for myself, except Idont know where to begin.

Any ideas?

Thanks very much.

 

[nos]

I am referring tot point charges.

 

[jtbell]

http://en.wikipedia.org/wiki/Magnetic_monopole#Maxwell.27s_equations

I remember seeing something similar to these "extended Maxwell's equations" in Halliday & Resnick's "Fundamentals of Physics" when I was a college freshman many years ago. Probably the only difference was in the units (SI versus cgs).

 

[nos]

Oh thans you, but I am interested in solving them tot get the Electric and magnetic field in terms of q(e) and q(m) and position, velocity and acceleration. I guess for each field you het two terms: because now both electric charge and magnetic charge create electric field and magnetic field.

 

[PJC01]

I am unable to provide a definitive answer as to how the Maxwell equations would be solved if magnetic monopoles exist. The existence of magnetic monopoles is still a topic of ongoing research and there is currently no experimental evidence to support their existence.

However, if we were to assume that magnetic monopoles do exist, then your approach of adding the fields generated by electric and magnetic charges separately would be a valid solution. This is because the Maxwell equations are based on the principle of superposition, which states that the total field at any point is equal to the vector sum of the individual fields generated by each charge.

Additionally, it is important to note that the Maxwell equations are not the only set of equations used to describe electromagnetic phenomena. There are other theories, such as the Yang-Mills theory, that can accommodate the existence of magnetic monopoles. Further research and experimentation would be needed to fully understand the implications of magnetic monopoles on our current understanding of electromagnetism.

If you are interested in exploring this topic further, I suggest studying the properties and behavior of magnetic monopoles and their potential effects on the Maxwell equations. You could also look into the work of researchers who are actively studying this topic and see if there are any experimental or theoretical approaches that have been proposed. Good luck with your exploration!