# The behavior of electromagnetic waves in matter

In vacuum, the $$\vec{E}$$ and $$\vec{B}$$ field are always perpendicular, in phase, and they travel at the speed of light $$c=3\times 10^8 \text{m/s}$$. I would like to know what happens in matter ? Do the same rules apply ?

• Electromagnetic waves will always have perpendicular $\vec E$ and $\vec B$ components traveling in phase. For the value of $c$, you may want to read about Refractive Index. – Sam Jul 3 '20 at 11:18

## 1 Answer

The wave equation $$\frac{\partial^2 \mathbf E}{\partial t^2} = c^2 \frac{\partial^2 \mathbf E}{\partial \mathbf x^2}$$ can be obtained from the Maxwell equations, for no charges or currents.

In vacuum, $$c^2 = \frac{1}{\mu_0\epsilon_0}$$.

For a transparent and isolant material as glass, with no free charges or currents, the same derivation is possible.

The only difference is that $$\mu_0$$ is replaced by $$\mu$$ and $$\epsilon_0$$ by $$\epsilon$$. So the wave speed changes, and is smaller than $$c$$.