The average of cos 2θ or sin 2θ gives 1/2. The Poynting vector, or the intensity, can be given as, 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). The time average of the energy flux is the intensity of the electromagnetic wave, which is the power per unit area. Most measuring devices, including our eyes, detect only an average over many cycles. The energy flux for visible light through any area is an extremely rapidly varying quantity. For a plane electromagnetic wave with E 0 and B 0 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:Īs the frequency of the electromagnetic wave is very high, for example, the frequency of visible light is in the order of 10 14 Hz, the energy flux rapidly varies with time. 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. The intensity can be expressed in terms of the maximum electric field (peak electric field) and maximum magnetic field (peak magnetic field) or by using the. The intensity formula depends on pressure and the area on. Using the relationship between fields and the speed of light, the equivalent expressions for intensity can be defined in terms of the magnitudes of the electric and magnetic fields alone. Intensity is the quantity of energy the wave conveys per unit time across a surface of unit area. By integrating the Poynting vector magnitude over a wave period, the expression for the intensity can be obtained. Then, the Poynting vector points in the positive x-direction.īy replacing the fields with wave functions, the expression for the Poynting vector can be rewritten.Īs the fields are mutually perpendicular, the Poynting vector magnitude equals the product of the peak amplitudes of the fields and a square of cosine term. Taking the time average of the Poynting vector gives the wave's intensity.Ĭonsider a plane electromagnetic wave with the electric field oscillating along the y-axis and the magnetic field along the z-axis.

The energy flow given by the Poynting vector is parallel to the plate. When a capacitor is connected to an alternating current, the direction of the electric field between the plates changes with time, which induces a varying magnetic field.

Intensity of light wave equation