# Maxwell's Equations - Tensor form

1. Jan 21, 2016

### IAN 25

1. The problem statement, all variables and given/known data
The gauge ∂tχ - A =0 enables Maxwell's equations to be written in terms of A and φ as two uncoupled second order differential equations. However, when the lorentz condition div A = 0 is applied, we are told the equation can be encapsulated as: one tensor equation ∂μFμA = jμ where j is the covariant 4 current. Written out longhand this is:

2φ/∂t2 - ∇2A

which is one coupled second order differential equation in A and φ. What happened to the terms ∂2A/∂t2 -∇2φ. Which were in the uncoupled version?

2. Relevant equations

3. The attempt at a solution

2. Jan 26, 2016