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.
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?