Problem — Radiation pressure and comet tails

Problem

Why does an electromagnetic wave exert a pressure on the surface that receives it? Discuss the case of a comet, whose dust tail points in the direction opposite the Sun.

Solution

Why there is a pressure. EM radiation carries momentum as well as energy. For a photon of energy $E$ the momentum is $p=\frac{E}{c}$ When the radiation hits a surface and is absorbed, it delivers all of its momentum: like a hail of bullets, it exerts a force and hence a pressure. The radiation pressure on an absorbing surface is $P_\text{rad}=\frac{I}{c}$ where $I$ is the intensity of the wave. If the surface is perfectly reflecting, the momentum is reversed and the pressure doubles: $P_\text{rad}=\frac{2I}{c}$

The case of the comet. The Sun radiates in all directions. On the tiny dust particles of the comet, radiation pressure (together with the solar wind, a stream of particles) exerts a push directed radially outward, i.e. away from the Sun. This is why the dust tail always points away from the Sun, regardless of the direction the comet is moving along its orbit.

Summary $p=E/c$; when absorbed it delivers it $\to$ $\ev{P_\text{rad}=I/c}$ (doubled if reflected). On the comet this push always orients the tail away from the Sun.

Radiation carries momentum

Collegamenti

Argomenti: Onde elettromagnetiche Concetti: Pressione di radiazione · Fotone