Charged sphere vs. modern 2-plate capacitors
+ + +___--- ---___ + Half of the (+) particles / -||+ \ on B dive into the gap, +| -||+ |+ but they induce charges | -||+ | of identical polarity +| -||+ | to appear on the OUTER | -||+ |+ surface of hemisphere A. +\___ -||+ ___/ --- --- + A + + B
We put no charges on hemisphere A, yet as far as the world outside the
narrow gap is concerned, A is now charged. The narrow gap makes A and B
interact strongly. It SEEMS as though there has been a current between A
and B. This "current" caused half of our 12 positive charges to travel to
the OUTER SURFACE of A. They didn't jump the gap. This wasn't an
electric current, but the end result is almost exactly the same as if
charges had crossed the gap. To a first approximation, charge has
flowed THROUGH the capacitor.
So, see why "Displacement Current" is not easily removed from capacitor
Also, look at this below. Suppose I ignore the closely-spaced charges
and short-range e-fields in the gap. This isn't forbidden. After all, to
an outside instrument the gap is tiny and its fields are vanishingly small
in comparison to the fields associated with those charges on the outer
surface. I could adjust the gap size to subatomic dimensions, which would
raise the capacitance to kilofarads or higher, and essentially produce
+ + +___--------___ + / \ +| |+ | | +| | | |+ +\___ ___/ -------- + + +
By attempting to charge one plate, we have essentially charged our entire
capacitor. This has implications for real-world capacitors. Suppose we
take a large-value capacitor and try to place a microcouloumb upon just
one plate. The result? The capacitor ends up (ahem!) "electrified," (not
"charged!") with half a microcoulomb on each face within the gap.
Perhaps a few volts appears across the capacitor's leads. But the full
microcoulomb also appears on the surface of the capacitor's outer case.
A typical capacitor has *picofarads* from its plates to distant ground.
Therefor a FEW HUNDRED THOUSAND VOLTS appears upon the entire capacitor
with respect to ground. Clearly we cannot put charge on just one plate of
a typical real-world capacitor.
Our capacitor acts very much like a wire. If I tried to put a 1 uC charge
on a short wire, I would expect hundreds of kilovolts to appear on the
wire with respect to distant ground. Or, if I place charge upon one end
of the wire, the charge immediately should distribute itself along the
entire wire. Just like it did with my hemispheres-capacitor.
Capacitors are not wires. However, their actions are very close to those
of wires. Imagine a capacitor like this:
__________________________________________ | | | |____________________|_____________________| /\ | | | Incredibly narrow slot
If I place charges on one end, as far as an outside observer is concerned
they will redistribute themselves along the entire surface. If I hook the
above "wire" into a circuit, and if I cause a loop of current to appear in
that circuit, charge will flow through the "wire." THROUGH it?
Now at the end of my speil I will add the traditional capacitor effects
back in. If I cause a charge to flow through the above wire, opposite
charges will be trapped within the gap, and a potential difference will
grow between the two halves. Current in one side of the "wire" forces an
equal current to appear in the other side of the "wire" via electrostatic
induction. If the current is constant with time, then the potential
difference across the halves will increase linearly with time.
Capacitors do not act like two separate metal objects. As far as currents
are concerned, they almost act like a "short circuit." They act like
conductors, but they have an interesting "back pressure effect" which
grows with time.