Question

Do electromagnetic waves carry momentum and energy?

Answer 1

Hint: Frequency and wavelength play a major role in how much energy or momentum does a wave carry. A wave whether it be an electromagnetic or a mechanical wave has a definite wavelength and frequency.

Complete step by step answer:
Electromagnetic waves as we all know has a definite wavelength and frequency and both of these quantities are related by the equation \[c=\nu \lambda \], where c is the velocity of light in the free medium, $\nu $ is the frequency of the E.M wave and $\lambda $ is the wavelength.

The momentum of an electromagnetic wave is given as by the formula,

$P=\dfrac{E}{c}$

Where, E is the energy of the electromagnetic wave. P is the momentum associated with the wave and c is the velocity of light.

The energy of an electromagnetic wave can be written as, $E=h\nu $, where h is the Planck’s constant and $\nu $is the frequency of the wave. So the momentum can be written as,
$P=\dfrac{h\nu }{c}=\dfrac{h}{\lambda }$

So, if we know the wavelength of an electromagnetic wave, we can determine the momentum of an electromagnetic wave.

As we all know that electromagnetic waves consist of both electrical and magnetic fields in which both has an energy density associated with them and the sum of them is the energy density of the electromagnetic wave given by,

${{\text{U}}_{\text{E}\text{.M}}}=\dfrac{1}{2}{{\varepsilon }_{0}}{{E}^{2}}+\dfrac{1}{2{{\mu }_{0}}}{{B}^{2}}={{\text{U}}_{\text{E}}}\text{+}{{\text{U}}_{\text{M}}}$

Where,

${{\text{U}}_{\text{E}}}$ is the energy density of the Electrical part of the E.M wave.
${{\text{U}}_{\text{M}}}$ is the energy density of the magnetic part of the E.M wave.

So this energy density associated with the electromagnetic wave shows that the electromagnetic waves carry energy while it travels through space.

Maxwell predicted that an electromagnetic wave carries momentum. An object absorbing an electromagnetic wave would experience a force in the direction of propagation of the wave. The force corresponds to radiation pressure exerted on the object by the wave. This radiation pressure is similar to momentum and this principle is responsible for the tail of the comets. As the sun’s radiation hits the comet, it applies a radiation pressure on the ionic particles of the comet and the tail is formed.

Note: The radiation pressure of light which is an E.M wave can be used to move satellites or spacecraft in space provided it has a large surface area to reflect light. Light sail programme by NASA is an example of this kind of experiment.

If an object absorbs an electromagnetic wave which has a definite momentum, then in order to conserve the momentum, the object gains some momentum from the wave.

The radiation pressure applied by a wave which is reflected off of a surface of an object is twice as that of the radiation pressure that the wave exerts on an object if the wave is absorbed by the object.