# EM wave field strength and energy

Usaf Moji
Another noobish question: Let's say there is an electromagnetic wave of constant wavelength and constant peak amplitude that travels a known distance. Let's say that we also know the total energy of this EM wave. Is there some formula that can tell us what the peak value of the electric field is (or the peak value of the magnetic field, it doesn't matter which)?

All responses appreciated.

## Answers and Replies

The energy density of an EM wave is given by $$\epsilon E^{2}+ \mu H^{2}$$ where $$\epsilon$$ is the permittivity, $$\mu$$ the permeability, E the electric field amplitude, and H the magnetic field amplitude. For the majority of cases, the magnetic component is much less than the electric component, B ~ E/c, and can be neglected.

Mentor
Actually, in an EM wave, in vacuum at least, the energy density is equally distributed between the electric and magnetic portions of the wave. The electric and magnetic energy densities in vacuum are

$$u_E = \frac{\epsilon_0 E^2}{2}$$

$$u_B = \frac{B^2}{2 \mu_0}$$

In an EM wave, B = E/c and

$$c = \frac{1}{\sqrt{\epsilon_0 \mu_0}}$$

which allow you to show that $u_E = u_B$.

Usaf Moji
Thank you Andy and jtbell, that was very helpful.