# Symmetries and Maxwells equations

Hi

Maxwells Equations for a time-invariant system are separable, hence we can write a solution as E(r, t) = E(r)E(t). They also mention that if the system is radially invariant, then that implies that the solution splits into a product of radial and angular functions (with 2π periodic angular functions).

Is it a general rule that when the system described by Maxwells equations has a symmetry, then the solutions become separable? If yes, does this go beyond Maxwells Equations?

Best,
Niles.

## Answers and Replies

Staff Emeritus
No. It's only true for 1/r and r2 potentials.

Thanks. Where does that spatial dependence come into play when looking at Maxwells Equations? Is in through ε(r)=n(r)2?

Do you have a suggestion for a reference that explains this in more details?

Best,
Niles.