Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/423

 

for the case of a simple harmonic disturbance in one plane. This corresponds to a ray of plane-polarized light, but whether the plane of polarization corresponds to the plane of the magnetic disturbance, or to the plane of the electric disturbance, remains to be seen. See Art. 797.

 

Energy and Stress of Radiation.

792.] The electrostatic energy per unit of volume at any point of the wave in a non-conducting medium is

${\frac {1}{2}}fP={\frac {K}{8\pi }}P^{2}=\left.{\frac {K}{8\pi }}{\frac {\overline {dF}}{dt}}\right|^{2}$.

(22)

The electrokinetic energy at the same point is

${\frac {1}{8\pi }}b\beta ={\frac {1}{8\pi \mu }}b^{2}=\left.{\frac {1}{8\pi \mu }}{\frac {\overline {dF}}{dz}}\right|^{2}$

(23)

In virtue of equation (8) these two expressions are equal, so that at every point of the wave the intrinsic energy of the medium is half electrostatic and half electrokinetic.

Let $p$ be the value of either of these quantities, that is, either the electrostatic or the electrokinetic energy per unit of volume, then, in virtue of the electrostatic state of the medium, there is a tension whose magnitude is $p$, in a direction parallel to $x$, combined with a pressure, also equal to $p$, parallel to $y$ and $z$. See Art. 107.

In virtue of the electrokinetic state of the medium there is a tension equal to $p$ in a direction parallel to $y$, combined with a pressure equal to $p$ in directions parallel to $x$ and $z$. See Art. 643.

Hence the combined effect of the electrostatic and the electrokinetic stresses is a pressure equal to $2p$ in the direction of the propagation of the wave. Now $2p$ also expresses the whole energy in unit of volume.

Hence in a medium in which waves are propagated there is a pressure in the direction normal to the waves, and numerically equal to the energy in unit of volume.

793.] Thus, if in strong sunlight the energy of the light which falls on one square foot is 83.4 foot pounds per second, the mean energy in one cubic foot of sunlight is about 0.0000000882 of a foot pound, and the mean pressure on a square foot is 0.0000000882 of a pound weight. A flat body exposed to sunlight would experience this pressure on its illuminated side only, and would therefore be repelled from the side on which the light falls. It is probable that a much greater energy of radiation might be obtained by means of