Physical
forces from electromagnetism.
Ivor
Catt. 10 July 2011
Some years ago my co-author David Walton said he
thought e=mc2 could be derived from classical electromagnetic
theory. I then attempted to do this, and had some success, which I put on the www
in around 2004. 1 , 2 . It
involved a pulse travelling down a coaxial cable into a short circuit. When
reflecting at the short, there was magnetic field on one side only on the short, and electric current in the short. (If we ignored the
fact that the magnetic field is on one side only of the conductor,) the formula
F=Bil gave a force on the conductor and an equal and
opposite force on the TEM Wave. From this Ft, force x time (duration of
reflection), I derived the momentum of the pulse (F=ma > Ft=mv). Momentum being mv (actually
mc) we thence get m. It links from
the already found energy e=vit to give e=mc2.
A few days ago
I realized that if the pulse reflects at an open circuit instead of a short,
there must have been the same force on the TEM Wave, this time supplied by
space rather than by the wire short. This is strange. However, more strangeness
flows today, leading to a very rich field for further investigation and
discovery.
If the pulse reflects at a short, there is presumably
a force to the left on the reflecting pulse, and a force to the right on the
short equal to F=Bil. (If a transformer has a shorted
turn it explodes outwards, so this correlates with a force to the right on our
shorting wire.)
The new discoveries come from considering the two
conductors in the section of coax near the short. Consider the short period
when some of the reflecting “pulse” overlaps the rear end, forward travelling
part of the “pulse”. There is a brief outwards force on the conductors. 1 , 2 .
However, reflecting from an open circuit, there is a brief force of attraction.
Thus, the force at the end is not reversed for open and short, but the lateral
force on the coaxial conductors is
reversed. 1 , 2
, 3
, 4 , 5 .
13 November 2011.
http://en.wikipedia.org/wiki/Radiation_pressure
Radiation
pressure is the pressure
exerted upon any surface exposed to electromagnetic radiation. If absorbed,
the pressure is the power flux density divided by the speed of light. If the radiation is
totally reflected, the radiation pressure is doubled. For example, the
radiation of the Sun at the Earth has a power flux density of 1,370
W/m2, so the radiation pressure is 4.6 µPa
(absorbed).
It is
known that if light is reflected by a mirror, the pressure is twice as large as
if it is absorbed. Similarly, if a TEM pulse
is absorbed in a correctly terminating resistor, the current in the resistor is
half the current in a short, leading to half the force on a resistor compared
with the force on a short.
This all
works out nicely until we consider the force causing a reflection from an open
circuit at the end of a coaxial cable. Where does it come from?
http://www.ivorcatt.co.uk/x0203em.htm
http://www.electromagnetism.demon.co.uk/785.htm
