What Is the Instantaneous Energy Density in the Electric Field of the Wave?

Definition

• Both the electric field and the magnetic field in an electromagnetic wave carry energy. The standard measurement of the energy they carry is energy density. Energy density is the amount of energy contained within a given volume of space. The instantaneous energy density is the energy in a particular volume of space at a particular moment. Because electromagnetic waves are composed of time-varying fields, the energy they contain at one location changes from moment to moment.

The Electric Field

• To determine the instantaneous energy density of the electric field, you must first determine what the electric field itself is at an given instant. The exact form that the formula takes depends on the coordinate system you use to describe it. If you choose a Cartesian coordinate system and orient it so that the wave is traveling along the x-axis, then the electric field is described by the equation E=E0cos(kx-wt). E is the amplitude of the electric field at time t and distance x from the origin. E0 is the maximum amplitude of the electric field. This is the amplitude that the field has right at its source. The k represents the value of two times pi divided by the wavelength of the wave. The w represents two times pi times the frequency of the wave.

Calculating the Instantaneous Energy Density

• The instantaneous energy density of an electric field is equal to the amplitude of the electric field at that instant, multiplied by itself. The result is then multiplied by the permitivity constant and divided by two. The permitivity constant is a measurement of how well electric fields travel through different materials. It has a different value for every material, as well as for empty space. To determine it, look up the value for the material that the wave you are studying is traveling in on a permitivity table.

Relationship with Wave Intensity

• The instantaneous energy density of the electric field allows you to easily find the intensity of the wave at any point in time. To find the instantaneous intensity of the wave, just multiply the instantaneous energy density of the electric field by the speed of light.