Prove that EMW are transverse in nature and also find the energy density of EMW and Poynting vector
Electromagnetic waves consist of time varying electric and magnetis fields which are mutually perpendicular to each other as well as to the direction of propagation of wave. i.e. electromagnetic waves are transverse in nature.
To prove the transverse nature of electromagnetic waves, we have to prove both electric and magnetic fields are perpendicular to the direction of wave propagation.
Consider a plane electromagnetic wave propagating along the positive x-axis direction and a parallelopiped OABCDEFG placed with its edges parallel to the three coordinate axes. The electric ang magnetic fields vary sinusoidally with x and t and are independent of y and z
Parallelopiped does not enclose any charge .According to Gauss’ law, the total electric flux across it must be zero.i.e.