Electromagnetic Wave Intensity

Introduction :

The electromagnetic wave intensity is nothing but the measure of the intensity of the electromagnetic wave in free space or in any medium. It generally depends on the velocity of the electromagnetic wave. It is proportional to the square of the amplitude of the electric or magnetic field.

Before giving a proper definition of electromagnetic wave intensity we first try to understand what electromagnetic waves are. The electromagnetic waves are nothing but the waves produced due to an accelerating or oscillating charge. This wave contains both electric and magnetic field vectors which are perpendicular to each other as well as perpendicular to the direction of the wave propagation.

Define Electromagnetic Wave Intensity:

The electromagnetic wave intensity is defined as the energy crossing per second per unit area perpendicular to the direction of propagation of electromagnetic wave or the average power per unit area transported by an electromagnetic wave.

Example of Electromagnetic Wave Intensity:

For proper understanding of the electromagnetic wave intensity, we consider an example in which the electromagnetic waves are propagated along X-axis with the speed of light. Consider an imaginary cylinder along the X-axis with area of cross section A and length c Δt and the electromagnetic waves are incident normally to the area A and crosses the cylinder as shown in Fig.1. Let u_av be the average energy density of the electromagnetic wave.

         Fig.1 Imaginary cylinder
The energy of electromagnetic wave (U) crossing the area of cross section at P normally in time Δt is the energy of wave contained in a cylinder of length c Δt and area of cross section A. It is given by
                                                            U =u_av (c Δt) A
The intensity of electromagnetic wave at P is
                                                            I = U / A Δt
                                                              = u_av c Δt A / A Δt
                                                              = u_av c
In terms of maximum electric field
                                                            u_av = ε₀ E₀² / 2
so,                                                        I = ε₀ E₀² c / 2 = ε₀ E²_rms c
In terms of maximum magnetic field
                                                            u_av = B₀² / 2μ₀
so,                                                        I = B₀² c / 2μ₀ = B²_rms c / μ₀