John Berry wrote:
Horace, thank you for your detailed analysis.
The reason I was asking was because I thought that if the forces are as Grassmann insists are perpendicular then removing the battery and instead using high frequency alternating current in what is now an open circuit should give rise to thrust.
------------------------------------------------------------------------- + ~ -
I
I
------------------------------------------------------------------------- - ~ +
The force on the I's would be perpendicular with no force on any other segment.
However with further thought, the only way the above would fail to generate thrust is if the forces are as Ampere claims (longitudinal) without any displacement current in the vacuum between the two rails.
Even if Ampere is correct as long as there is displacement current the magnetic force from the vacuum displacement current would push on the rail in a longitudinal manner.
It's worth keeping in mind that EM theory can be built up using the principle of superposition and a knowledge of how just two moving (accelerated) charges interact.
In the case of a two-charge system, momentum is conserved, if one takes account of the momentum of the EM field radiated by the charges (assuming the charges are accelerated). And a system of just two interacting charges is pretty well understood, experimentally and theoretically, I think.
So, unless one cares to discard the principle of superposition, one must conclude that momentum will be conserved in the case of a rail gun as well. So, the momentum you gain as the physical structure is propelled to the left must be exactly balanced by the momentum of the EM radiation the system is going to send out as the current in the system changes.
In other words, it'll work, no doubt about that. But the thrust will be exactly analagous to the recoil felt by a directional radio antenna -- it will be equal and opposite to the momentum carried off by the radio waves being generated as the capacitor is charged.
(I don't pretend to be able to match Horace's knowledge of the details here, of course! I just thought an intuitive comment about how and why the momentum equation still balances might be apropos.)
