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33.11:

Momentum And Radiation Pressure

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Momentum And Radiation Pressure

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Electromagnetic waves transport momentum while traveling through space. The corresponding momentum density is expressed in terms of the Poynting vector magnitude and the speed of light.

By substituting the volume occupied by the wave that passes through an area in a short interval of time, the momentum flow rate per unit area can be obtained.

The average rate of momentum transfer per unit area is obtained by replacing the average value of the Poynting vector with intensity.

Due to the transfer of momentum, electromagnetic waves exert pressure on the surface, known as radiation pressure.

Now, the average rate of change of momentum equals average force and force per unit area is the radiation pressure.

Thus, the radiation pressure is directly proportional to the intensity of the wave.

If the surface perfectly absorbs the electromagnetic wave, the corresponding momentum is also transferred completely to the surface.

For a perfectly reflecting surface, the momentum change will be double. Thus, the radiation pressure also doubles. 

33.11:

Momentum And Radiation Pressure

An object absorbing an electromagnetic wave would experience a force in the direction of propagation of the wave. This force occurs because electromagnetic waves contain and transport momentum. The force accounts for the wave's radiation pressure exerted on the object. Maxwell's prediction was confirmed in 1903 by Nichols and Hull by precisely measuring radiation pressures with a torsion balance. The measuring instrument had mirrors suspended from a fiber kept inside a glass container. Nichols and Hull obtained a slight measurable deflection of the mirrors from shining light on one of them. From the measured deflection, they calculated the unbalanced force on the mirror and obtained an agreement with the predicted value of the force. The radiation pressure applied by an electromagnetic wave on a perfectly absorbing surface turns out to be equal to the energy density of the wave. Suppose the material is perfectly reflecting, and the electromagnetic waves are incident normal to the surface. In that case, the pressure exerted is twice as much because the direction of momentum reverses upon reflection.

Radiation pressure plays a role in explaining many observed astronomical phenomena, including the appearance of comets. When a comet approaches the Sun, it warms up, and its surface, composed of frozen gases and particles of rock and dust, evaporates. The comet's coma is the hazy area around it made up of the gases and dust. Some of the gases and dust form tails when they leave the comet. The ion tail is composed mainly of ionized gases. These ions interact electromagnetically with the solar wind, a continuous stream of charged particles emitted by the Sun. The force of the solar wind on the ionized gases is strong enough that the ion tail almost always points directly away from the Sun. The second tail is composed of dust particles. Because the dust tail is electrically neutral, it does not interact with the solar wind. However, this tail is affected by the radiation pressure produced by the light from the Sun. Although relatively small, this pressure is strong enough to cause the dust tail to be displaced from the comet's path.

Suggested Reading

  1. OpenStax. (2019). University Physics Vol. 2. [Web version]. Retrieved from 16.4 Momentum and Radiation Pressure – University Physics Volume 2 | OpenStax