I have several problems following this paper, but for now I will point out one really glaring (to me) error.
In the paragraph following Eq 10, the authors state that the "enclosed charge" in Gauss' law ( or in Div E = rho) is (and is only) the charge which sources the E field being referenced. This is not true! Div E = rho is true whatever are E and rho at a given space-time point - period.
On Jun 5, 2009, Carl Mungan <mungan@usna.edu> wrote:
I found the following paper to be a bit startling. Did anyone else notice it:
Rothman & Boughn "The Lorentz force and the radiation pressure of
light," AJP vol. 77, p. 122 (Feb 2009)
The gist of it is they claim the familiar derivation of radiation
pressure in intro texts is wrong.
To remind you of this derivation, it goes as follows: An EM plane
wave is normally incident on a conductor, say E in the x direction, B
in the y direction, propagation in the z direction. Consider a free
electron on its surface, initially at rest. The E field pushes the
electron in the -x direction so it acquires velocity v in that
direction. Then -e(v x B) is in the +z direction, giving radiation
pressure.
The authors go through this derivation more carefully than intro
texts and show it doesn't work if you're less cavalier.
Next comes a section called "Interpretation" which I can't fully
follow, but the upshot of which is that radiation reaction is a
necessary part of the real story. Skipping over that, they
nevertheless then give an alternative "elementary" approach involving
the boundary conditions for E and B at the surface and indicating
that an induced surface current is involved (although there is a
subsequent remark about "no Munchausen effect" that seems to weaken
their development in my mind).
Anyhow, the bottom line is: They've convinced me that the traditional
"derivation" is bogus; they've confused me about what the real story
is; and they've given me an alternative approach that I wish could be
further simplified if I'm going to use it in an intro course.
I'd be mighty interested in what the rest of you think about all this. -Carl
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