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Re: Force on a Capacitor Plate



At 01:17 PM 2/17/01 -0600, Doug Craigen wrote:
Suppose you measure the force on the plate of an air-filled capacitor
held at a fixed potential difference - call that Fo. Now fill all
relevant surrounding space with a dielectric liquid of permittivity e_r
. The capacitance increases by a factor of e_r, hence the charge on the
plates increases by the same, but the E field is unaffected - so the
standard textbook answer is that the new force on the plate is e_r*Fo.

I am curious as the whether this is physically what would be observed.
Has anybody here tried the measurement?

No, but I have great faith in the principle of virtual work, i.e.
F_x = - d(Energy) / dx

....
it would have the
liquid pushing against it with a force of (1-e_r)*Fo, so the force you
would actually measure would still be Fo.

Where does this liquid force come from? If it represents a pressure in the
liquid, proportional to electric field, then
a) That's remarkable new physics, and
b) That's going to cause very weird things to happen at the edge of the
capacitor, where there are field gradients and therefore, I assume,
gradients in the alleged pressure.

OTOH if it does not represent a pressure in the liquid, then there's going
to be a violation of Newton's laws, which is perhaps best seen as a
violation of conservation of momentum. Force is momentum per unit
time. Imagine the flow of momentum into little cells of liquid right next
to the capacitor plate, in proportion to the force that the liquid is
allegedly exerting on the plate. Now, if momentum is conserved, where does
all that momentum go to? That is, how do you "close the circuit" of
momentum flow?

Bottom line: I think the alleged liquid force doesn't exist.