(1044) |

But, what actually causes the car to move? If the radiation possesses momentum
then the car will recoil with the same momentum as the radiation is emitted.
When the radiation hits the other end of the car then the car acquires momentum
in the opposite direction, which stops the motion. The time of flight of
the radiation is . So, the distance traveled by a mass with momentum
in this time is

(1045) |

Thus, the momentum carried by electromagnetic radiation equals its energy divided by the speed of light. The same result can be obtained from the well-known relativistic formula

(1047) |

(1048) |

(1049) |

Thus, the momentum density equals the energy flux over .

Of course, the electric field associated with an electromagnetic wave oscillates
rapidly, which implies that the previous expressions for the energy density,
energy flux, and momentum density of electromagnetic radiation are also
rapidly oscillating. It is convenient to average over many periods of
the oscillation (this average is denoted
). Thus,

where the factor comes from averaging . Here, is the peak amplitude of the electric field associated with the wave.

Since electromagnetic radiation possesses momentum then it must exert a force on
bodies which absorb (or emit) radiation. Suppose that a body is placed in
a beam of perfectly collimated radiation, which it absorbs completely. The amount
of momentum absorbed per unit time, per unit cross-sectional area, is simply the
amount of momentum contained in a volume of length and unit cross-sectional
area: *i.e.*, times the momentum density . An absorbed momentum per
unit time, per unit area, is equivalent to a pressure. In other words, the radiation
exerts a pressure on the body. Thus, the *radiation pressure* is given by

Consider a cavity filled with electromagnetic radiation. What is the radiation
pressure exerted on the walls? In this situation, the radiation propagates in
all directions with equal probability. Consider radiation propagating at an
angle to the local normal to the wall. The amount of such radiation
hitting the wall per unit time, per unit area, is proportional to .
Moreover, the component of momentum normal to the wall which the radiation
carries is also proportional to . Thus, the pressure exerted on the
wall is the same as in Eq. (1054), except that it is weighted by the
average of over all solid angles, in order to take into account
the fact
that obliquely propagating radiation exerts a pressure which is
times that of normal radiation. The average of over all solid angles
is , so for isotropic radiation

(1055) |

The power incident on the surface of the Earth due to radiation emitted by
the Sun is about Wm. So, what is the radiation pressure?
Since,

(1056) |

(1057) |

The radiation pressure from sunlight is very weak. However, that produced by
laser beams can be enormous (far higher than any conventional pressure which
has ever been produced in a laboratory). For instance, the lasers used in Inertial
Confinement Fusion (*e.g.*, the NOVA experiment in
Lawrence Livermore National Laboratory)
typically have energy fluxes of Wm.
This translates to a radiation pressure of about atmospheres!