Coupled PDEs - all 4 Maxwell's equations?

[VictorVictor5]

Greetings all,

Quick question. I know that all 4 Maxwell's equations are said to be first-order, coupled PDEs, where each equation has an unknown field. I see that with Faraday's and Ampere's law, because, E and H appear in each of those equations.

But Gauss' laws, I'm not seeing that, since they're both equal to electric/magnetic charge densities (or 0 in the case of the magnetic law due to there not being magnetic monopoles).

So, are Gauss' laws coupled? And do they still have the unknown fields? Sorry I am not seeing this. I just need a quick "reality check" here.

Thanks!
VV5

 

[aabottom]

Yes, all 4 Maxwell's equations are coupled. This may be hard to see since they are usually written with notation using 4 different fields, E, B, D and H, plus the current density J. The coupling become more apparent when considering the constituent equations:
1) D = epsilon * E
2) B = mu * H
3) J = sigma * E

Then all 4 Maxwell's equations can be written in terms of E, H, and the charge density, rho.