# Poynting's Theorem in Forms

1. Apr 17, 2010

### Phrak

In this PDF file, through some guess work, I propose a p-form equivalent of Poynting's Theorem and derive his expression in the tensor calculus--oops, I mean, vector calc. It happened to work.

https://dl.dropbox.com/u/6215524/Post%20of%20Notes%20on%20Poyntings%20Theorem.pdf" [Broken]

Pointing's equation of energy continuity appears as the temporal component of a 1-form.

G*dG + F*dF = FK–GJ, ​

F is the Faraday tensor with lower indices, and G=*F, the Hodge dual of F. J and K are the covariant charge/current density 4-vector duals; electric and magentic. Though derived in pseudo Riemann normal coordinates, it is true under general coordinate transforms.

In afterthought I think the p-form equations as well as Poynting's Theorem are at root physically meaningless, via the hidden invocation of magnetic and electric currents in propagating electromagnetic fields.