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# 33.12: Radiation Pressure: Problem Solving

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### 33.12: Radiation Pressure: Problem Solving

The radiation pressure applied by an electromagnetic wave on a perfectly absorbing surface equals the energy density of the wave. The wave's momentum also gets transferred to the surface when an electromagnetic wave is entirely absorbed by it. The rate at which momentum is transmitted to an absorbing surface perpendicular to the propagation direction equals the force on the surface.

The average value of the rate of momentum transfer divided by the absorbing area represents the average force per unit area or radiation pressure due to the wave. If the material is perfectly reflecting, such as a metal surface, and the incidence is along the normal to the surface, then the pressure exerted doubles because the momentum direction reverses upon reflection.

Sunlight exerts a far stronger radiation pressure inside the sun than it does on the Earth. Radiation pressure inside stars that are significantly more massive and brighter than the sun is so high that it greatly increases the internal gas pressure, preventing these stars from collapsing due to their own gravity. Sometimes, the radiation pressure of stars can significantly impact the material in their immediate vicinity.

Radiation pressure plays a role in explaining many other observed astronomical phenomena, including the appearance of comets. When a comet approaches the sun, it warms up, and its surface begins to evaporate. Some of the gases and dust form tails when they leave the comet. A comet has two tails; the first is the ion tail, composed mainly of ionized gases. These ions interact electromagnetically with the solar wind. 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 quite small, this pressure is strong enough to cause the dust tail to be displaced from the comet's path.