# Proof that electric and magnetic fields in a EM wave are perpendicular

Is there a general proof, that for electromagnetic waves the magnetic and electric fields are perpendicular? The only ones I can find only focus on plane waves.

• – Qmechanic Feb 12 '15 at 11:51
• Every wave is a superposition of plane waves (if the medium is well-behaved), so it suffices to show this for plane waves to show it for every wave. – ACuriousMind Feb 12 '15 at 15:53
• Since $\mathbf E\cdot \mathbf B$ is quadratic in the fields, appeal to linearity does not work. The statement is true for monochromatic waves and waves with definite polarisation. – Robin Ekman Feb 12 '15 at 16:37
• Surface waves Lower frequencies, below 3 MHz, travel efficiently as ground waves. This is because they are more strongly diffracted around obstacles due to their long wavelengths, allowing them to follow the Earth's curvature. The Earth has one refractive index and the atmosphere has another, thus constituting an interface that supports the surface wave transmission. Ground waves propagate in vertical polarization, with their magnetic field horizontal and electric field (close to) vertical. – Sofia Feb 12 '15 at 17:12
• Well, there are electromagnetic waves in plasmas where the electric and magnetic fields are not purely orthogonal to each other, so it is not surprising that you can only find examples for plane waves. Plane waves are well behaved, but not all waves are... – honeste_vivere Apr 24 '15 at 12:39