You mentioned your own tests in an attempt to prove whether or not an induced E-field can influence, or be influenced by a point charge. THAT is what the following referred to:
I wasn't referring to Gibbs' test question and diagram.
Ok, sorry!
If you want to measure the induced electric field in its non-integral form, you should use two small metallic balls spaced about 3/4" apart. If you want to measure the induced electric field in its non-integral form, you should use two small metallic balls spaced about 3/4" apart. They have magnet wire leads twisted together, which connect to a scope. Position the balls so that one is closer to the solenoid axis, and the other is radial outward. You will measure a difference in potential across the two balls.
Thuesday I asked the question of the effect of an induced current onto a point charge on 4 physics forums because I was tired of not mastering this subject. The threads are not yet ended but there is some progress.
When the balls are not far from one another, we can possibly show an effect. If we place the balls each side of the hole of the toroid, the effect is much stronger.
The reason that emerges from these experiments is that, in reality, this apparently open circuit is closed between the balls due to the displacement currents. Such circuits with open capacitors are in fact closed circuits. When the displacement currents cross totally or partially the hole of the toroid, the circuit is looped around the magnetic flux, therefore a current can be detected.
In my first experiment, the displacement currents through the toroid hole should have been very weak, question of solid angle that represents the hole viewed from the capacitors, comparing to the whole space where the displacement currents can travel from one capacitor to the other one.
In the experiment that you propose, the position of the balls is better than in mine for the propagation of the displacement currents through the hole because one ball is placed on the axis.
But the conclusion is still that there is strictly no effect when the circuit is looped without flux crossing it. This is a direct consequence of theory: according to Stockes theorem, the surface integral of the curl of a vector field over a surface is linked to the line integral of the vector field over its boundary. As B=rot(A) and B=0, the line integral of the vector E-field on any closed circuit where B=0 is null.
Now that we know that
- we can't expect for an induced current in a closed circuit placed outside a toroid, and
- a "dipole circuits" with terminal capacities is closed thanks to the displacement currents and thus doesn't provide more emf than the part due to the flux through the "leakage circuit" created by the displacement currents through the toroid hole,
well, we have to reinvent a completly new kind of experiments . The ideal would be to observe the effect of a toroid coil on single charges in vacuum. Not easy for a small lab...
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Topic: Professor Walter Lewin's Non-conservative Fields Experiment (Read 312883 times)
