# Poynting Vector at an interface with no free current flowing

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1. Sep 30, 2015

### Jon.G

1. The problem statement, all variables and given/known data
How do the normal and tangential components of the Poynting vector in matter, S = E x H , behave at an interface between two simple media where no free current flows, but either free charge or polarization charge is present at the interface?

2. Relevant equations
E1(para) - E2(para)0

3. The attempt at a solution
Honestly, I'm having trouble starting this. Think I might just need a nudge in the right direction though.

I think I know what to do, but doing it is a different question :S
I think I should probably write E and H as the sum of their parallel and perpendicular components and then substitute this into the equation for the Poynting Vector (S), and then identify the parallel and perpendicular components of S.
(Surely it can't be as simple as E = Epara + Eperp and same for H)
Then I would somehow use the boundary conditions of the E and H vectors and apply this to S, but I'm not too sure how to do this.
The only boundary condition I can think of that I know is the one I wrote above.
I've also written that H is discontinuous by Jc but I do not know how to prove this (and the q states no free current flows)

This could be an insanely easy question I just feel like my mind is hitting a wall and I'm getting frustrated by how little I've got done :S

Thanks in advance for any help :)

2. Oct 5, 2015