# Why are electromagnetic waves transverse waves? Is this answer ok?

by Spinnor
Tags: electromagnetic, transverse, waves
 P: 292 You can use Maxwell's equations to show that a plane wave in free space is transverse. Imagine a plane wave travelling in the x direction, E(x,t). Gauss' law states $\frac{\partial E_{x}}{\partial x}=0$ since there is no field variation in the y,z directions. Ampere's law states $\mu_{0}\epsilon_{0}\frac{\partial E_x}{\partial t}=\frac{\partial B_z}{\partial y}-\frac{\partial B_y}{\partial z}=0$ for the same reason. So the component of E in the direction of propagation does not vary in space or time, ie the wave is transverse. Since you can represent a solution to the wave equation by a sum of plane waves, this is enough to show that EM waves are transverse in isotropic, homogeneous media.