# Why is the value of volume charge density $ρ$ zero in lossy medium?

Given is the page of a book which I was studying. I was trying to study the derivation of the wave equation in a lossy medium. As I have underlined a sentence that says, "most of the case in which wave is propagating does not contain the charges". Why is it so?

## 1 Answer

This is not true in all cases, but at least approximately valid in most lossy media. Note that even if $$\rho\ne0$$, it is only the gradient of the charge density ($$\vec\nabla\rho$$) that appears in the wave equation, so the wave propagation is unaffected by a uniform non-zero charge density. Even if $$\rho\ne0$$, its gradient is usually (but not always) small.

A lossy medium has non-zero conductivity, meaning charge carriers can get redistributed. For example, if at some point in time there is a large amount of charge localized in a region, the resulting electric field can quickly cause this charge to redistribute, until a zero charge density is reached.

Again, there are lots of counter examples, such as a pn-junction.