# Maxwell's equations and conservation principles

1. Apr 21, 2015

### Delta²

Once we define energy and momentum carried by the field , is it possible to derive Maxwell's equations from conservation of momentum and conservation of energy (along perhaps with conservation of charge)?

2. Apr 21, 2015

### Orodruin

Staff Emeritus
Once you have derived the energy momentum tensor, you essentially have the free Lagrangian density. From there you should be able to derive Maxwell's equations in vacuum. Add an interaction term for the equations with a source.

Conservation of energy and momentum is a consequence of invariance under time and space translations.

3. Apr 21, 2015

Staff Emeritus
How does that link E and B fields? (i.e. how do you know that you need to set up a vector potential and not just a scalar potential?) And how do you add the right source terms?

4. Apr 21, 2015

### Orodruin

Staff Emeritus
You are right in the fact that I have assumed that the electromagnetic field tensor is the exterior derivative of a one form, which of course already is half of Maxwell's equations.

With regards to the source, this is going to depend on the field you interact with. Regardless of what field that is, translational invariance should make the total energy momentum tensor conserved and thereby guarantee energy and momentum conservation.