Electromagnetic waves transport energy. This problem shows you which parts of the energy are stored in the electric and magnetic fields repsectively and also makes a useful connection between the energy density of a plane electromagnetic wave and the poynting vector.
In this problem we explore the properties of a plane electromagentic wave traveling at the speed of light c along the x axis through vacuum. Its electric and magnetic fields are as follows:
Throughout use these variables (E, B, ,k,x,) in answers. You will also need the permittivity of free space and the permeability of free space .
(a) What is the instantaneous energy density in the electric field of the wave?
(b) What is the instantaneous energy density in the magnetic field of the wave?
(c) What is the average energy density in the electric field of the wave?
(d) What is the average energy density in the magnetic field of the wave?
(e) Derive an expression for averafe enerhy density in the whole wave.
