# The relationship between material properties and EM wave frequency

Assuming an EM wave traveling inside an electrically neutral dielectric material. The following electric field describes the EM.

$$\vec{E}(t,x)=20\cos(\omega t-50x)\vec{u_y}$$.

Using the 3rd Maxwell equation, the associated magnetic field is derived as

$$\vec{B}(t,x)=\frac{10^3}{\omega}\cos(\omega t-50x)\vec{u_z}$$

then, using the 4th Maxwell equation, I got the equality

$$\mu\varepsilon=\frac{2500}{\omega^2}$$.

Does it mean that there is a dependency between the material properties ($$\mu$$ and $$\varepsilon$$) and the wave frequency? It seems to be a little bit strange since that $$\mu$$ and $$\varepsilon$$ usually are constants.

You have got the usual dispersion relation for an EM field $$\boldsymbol{E}=\boldsymbol{E}_{0} e^{i\left(\boldsymbol{k}\cdot\boldsymbol{r}-\omega t\right)}$$ in a linear material
$$\omega=ck$$
with $$c=\frac{1}{\sqrt{\mu\varepsilon}}$$ the speed of the wave. In your case $$k=50$$ is given, and therefore $$\omega$$ can be calculated.