Standing Electromagnetic Waves

Recall the standing waves formed in a tight string.

Standing waves are the combination of two waves that move in the opposite direction but have the same amplitude and frequency.

Consider a perfect conducting sheet placed in the y-z plane. A linearly polarized electromagnetic wave strikes the sheet, while traveling in the negative x-direction.

The incident wave induces the current on the surface of the conductor, resulting in additional electric fields, producing a reflected wave with the same frequency and amplitude as the incident wave.

The superposition of these two waves generates the standing wave. Simplifying these expressions provide the points on the wave where the magnitudes of the electric field and the magnetic field are zero. These are called the nodes or nodal planes.

An antinode is a point where the amplitude goes from the maximum positive to the maximum negative displacement.

The nodes of the electric field coincide with the antinodes of the magnetic fields, and vice versa. Hence, they are 90-degrees out of phase at each point.