33.10 : Intensity Of Electromagnetic Waves

The energy transport per unit area per unit time, or the Poynting vector, gives the energy flux of an electromagnetic wave at any specific time. For a plane electromagnetic wave with E₀ and B₀ as the peak electric and magnetic fields and traveling along the x-axis, the time-varying energy flux can be given by the following equation:

As the frequency of the electromagnetic wave is very high, for example, the frequency of visible light is in the order of 10¹⁴ Hz, the energy flux rapidly varies with time. The energy flux for visible light through any area is an extremely rapidly varying quantity. Most measuring devices, including our eyes, detect only an average over many cycles. The time average of the energy flux is the intensity of the electromagnetic wave, which is the power per unit area. It can be expressed by averaging the cosine function in the expression of over one complete cycle, which is the same as time-averaging over many cycles (here, T is one period). Hence, the average of

the Poynting vector, or the intensity, can be given as,

The average of cos²θ or sin²θ gives 1/2. Hence, the intensity of light moving at speed c in a vacuum is then found to be

The equivalent expressions for intensity are,