Re: Radiation Pressure

[jhowell@yang.earlham.edu (john howell)]

Rick Swanson sends:

> > John DaCorte asked:
> >
> > > What causes radiation pressure?
>
> This question gets right to the heart of one of introductory students'
> favorite questions, "If light doesn't have mass, how can it have
> momentum?"  Well, the story goes, light is composed of time varying
> electric and magnetic fields.  Fields describe forces on charges.
> Forces cause charges to accelerate.  So, charges which did not have
> momentum before interaction with light may have momentum after the
> interaction.  Ergo, if momentum is conserved, the light must have had
> momentum to start with.
>
> I remember, in the distant past, an elegant Maxwell's equation
> calculation of the interaction of an EM wave with charges which
> confirmed the appropriate relationships for momentum of light.
>
> Would appreciate comments illuminating this elementary explanation.
The overview is the explanation is this:  the light's E-field causes
charges to move.  The interaction between these moving charges and the
light's B-field causes a force, and the value of that force per-unit-area
is the pressure.

In more detail:   Suppose a wave of oscillating E and B fields hits a
conducting surface. For concreteness, suppose the light is moving along the
+x axis, that its E field is polarized along the y axis.  Its B field will
then be polarized along the +z axis.   When the E field interacts with
electrons in the conductor, it will force the electrons to oscillate along
the y axis.   These moving electrons constitute a current.  Because of the
B field, this current of moving electron will experience a "Lorentz" force:
F = q v X B.  When the current is along the y axis, and the B field is
along the z axis, this force will be parallel to the x axis.

Since electrons are negative, one must be a bit careful dealing with the
signs.  When E field in the light wave is in the +y direction, it will
force electrons in the metal to move in the -y direction.  At that same
instant, the B field will be in the +z direction, so  v X B will be in the
-x direction, so q v X B will be in the + x direction (because q is
negative).

Will the force reverse sign half a cycle later?  No.  Half a cycle later, v
and B will have reversed directions, so v X B will STILL be in the +x
direction.  Thus, even though the force varies because of the sinusoidal
oscillation in B and E, the forward force has a non-zero average.



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