What is this version of the wave equation?

[girlinphysics]

I came across this expression for the wave equation:

$$\nabla^2E + \mu\sigma\frac{\partial{E}}{\partial{t}} - \frac{n^2}{c^2}\frac{\partial{E}}{\partial{t^2}} = 0$$

My question is what kind of medium is it for/where did it come from?

 

[Chandra Prayaga]

That is the equation of an electromagnetic wave passing through a conducting medium. You wrote the last term wrong. It should be the second derivative of the electric field. You will see it in any book on classical electrodynamics.

 

[girlinphysics]

That is the equation of an electromagnetic wave passing through a conducting medium. You wrote the last term wrong. It should be the second derivative of the electric field. You will see it in any book on classical electrodynamics.

Where does the refractive index come from?

 

[Chandra Prayaga]

The medium has a refractive index and a conductivity.