Plane Electromagnetic Waves I

Consider an xyz coordinate divided into two distinct regions by a plane parallel to the yz plane.

A uniform electric and magnetic field in the +y and +z directions are present on the left side, while the right side is field-free.

This boundary plane, called a wavefront, moves in the +x direction with a constant speed.

Such waves where, at any instant, the fields are uniform over any plane perpendicular to the direction of propagation are called plane waves.

These waves satisfy Maxwell's equations. Consider a rectangular Gaussian box.

Since the electric field is along the y-direction, the electric fluxes for the surface along the x-direction and z-direction are zero.

For the top surface, the flux is opposite to the bottom surface, giving zero net flux.

Since the box encloses no electric charge, the electric as well as the magnetic flux is zero.

Thus, Gauss's law holds for electromagnetic radiation.

Therefore, the electric and magnetic field vectors are perpendicular to each other and to the direction of propagation, showing transverse nature.