33.9
Energy Carried By Electromagnetic Waves
Anyone who has used a microwave oven knows there is energy in electromagnetic waves. Sometimes, this energy is obvious, such as in the summer sun's wa…
The energy density corresponding to electric and magnetic fields of an electromagnetic wave is proportional to the square of the respective field magnitudes.
Thus, the total energy density equals the sum of the energy density of both fields. Using the relation between the fields, the expression for energy density shows that the energy due to the individual fields is equal and total energy density is double the energy density due to an individual field.
Now, consider an area perpendicular to the direction of propogation. The distance traveled and the energy passing through the volume in a small interval due to the wavefront can be determined.
From this, the energy flow per unit area per unit time, or the energy flux, can be obtained.
In general, energy flux is defined as the cross-product of the electric and magnetic fields. This quantity is known as the Poynting vector.
It is directed along the electromagnetic wave propagation, and its magnitude gives the rate of energy flow.
View the full transcript and gain access to JoVE Core videos
Q1: How does field strength relate to the energy carried by electromagnetic waves?
The energy carried by an electromagnetic wave depends directly on the strength of its electric and magnetic fields. Greater field strength means more work can be done and more energy the wave carries. Wave amplitude, which is the maximum field strength of both fields, determines the total wave energy in the electromagnetic wave.
Q2: What is energy density in an electromagnetic wave?
Energy density is the energy per unit volume of an electromagnetic wave, calculated as the sum of energy density from the electric field and magnetic field. Using the relationship between electric fields, magnetic fields, and the speed of light, these two energy densities are equal, making total energy density double the energy density of either individual field.
Q3: Why are electric and magnetic field energies equal in electromagnetic waves?
In electromagnetic waves, the electric and magnetic field energy densities are equal because of the fundamental relationship between electric fields, magnetic fields, and the speed of light. This relationship ensures that energy is equally distributed between both fields, so total energy density equals twice the energy density of one field alone.
Q4: What is the Poynting vector and what does it represent?
The Poynting vector is a vector quantity defined as the cross-product of electric and magnetic fields, representing energy flux or energy flow per unit area per unit time. It is directed along the electromagnetic wave propagation direction, and its magnitude gives the rate at which energy flows through a surface.
Q5: How is energy transported through space by electromagnetic waves?
Energy density moves with the electric and magnetic fields as the waves propagate through space. The rate of energy transport through a surface is defined by the Poynting vector, which indicates how much energy flows per unit area per unit time along the direction of wave propagation.
Q6: What determines how much energy an electromagnetic wave can deliver to a system?
The energy an electromagnetic wave delivers depends on the strength of its electric and magnetic fields. These fields exert forces on charges in a system and do work on them. Whether the energy is absorbed or not, the field strengths determine the wave's capacity to perform work and transfer energy.
Q7: How do you calculate total energy density in a traveling electromagnetic wave?
Total energy density in a traveling plane wave equals the sum of energy densities from the electric field and magnetic field. Since these individual energy densities are equal due to the relationship between fields and the speed of light, the total energy density is double the energy density of either field alone.