## Related questions with answers

An electromagnetic wave propagating in vacuum has electric and magnetic fields given by $\vec{E}(\vec{x}, t)=\vec{E}_0 \cos (\vec{k} \cdot \vec{x}-\omega t)$ and $\vec{B}(\vec{x}, t)=\vec{B}_0 \cos (\vec{k} \cdot \vec{x}-\omega t)$, where $\vec{B}_0$ is given by $\vec{B}_0=\vec{k} \times \vec{E}_0 / \omega$ and the wave vector $\vec{k}$ is perpendicular to both $\vec{E}_0$ and $\vec{B}_0$. The magnitude of $\vec{k}$ and the angular frequency $\omega$ satisfy the dispersion relation, $\omega /|\vec{k}|=\left(\mu_0 \epsilon_0\right)^{-1 / 2}$, where $\mu_0$ and $\epsilon_0$ are the permeability and permittivity of free space, respectively. Such a wave transports energy in both its electric and magnetic fields. Calculate the ratio of the energy densities of the magnetic and electric fields, $u_B / u_E$, in this wave. Explain.

Solution

VerifiedWe are given: -electric field in the propagating electromagnetic wave $\vec{E}(\vec{x},t)=\vec{E}_0\cdot \cos{(\vec{k}\cdot \vec{x}-\omega t)}$ -magnetic field in the propagating electromagnetic wave $\vec{B}(\vec{x},t)=\vec{B}_0\cdot \cos{(\vec{k}\cdot \vec{x}-\omega t)}$ -constant vector $\vec{B}_0$ is given by $\vec{B}_0=(\vec{k} \times \vec{E}_{0})/\omega$ -dispersion relation that $\vec{k}$ and $\omega$ satisfy: $\omega/|\vec{k}|=(\mu_0 \cdot \epsilon_0)^{-1/2}$

## Create an account to view solutions

## Create an account to view solutions

## More related questions

1/4

1/7