Re: Energy vanishing into air? (fwd)

[Steven Roys <sroys@xxxxxxxx>]

---------- Forwarded message ----------
Date: Sat, 17 Jan 2004 22:03:49 -0200
From: Antonio Carlos M. de Queiroz <acmq@xxxxxxxxxxxxxxxx>
To: High Voltage list <hvlist@xxxxxxxxxx>
Subject: Re: Energy vanishing into air? (fwd)

High Voltage list wrote:

> From: Alfred Erpel <alfred@xxxxxxxxx>

>     Imagine an air variable capacitor with plates fully engaged and the
> capacitor fully charged.
>
>     Let's use the example of .001µF charged to 10,000 volts. Stored energy =
> joules = .5CV^2 = .05 watt=seconds.
>
>     What happens to the energy of the fully charged capacitor when the
> plates are rotated to the 0µF capacitance position?

> [Potential energy.  It would take that much energy to rotate the cap
> plates to the 0uF position (barring friction losses), and rotating them
> back would convert the energy back from potential to the energy stored in
> the electrical field.  SRR]

Note also that the "0 uF" would never be reached. The minimum
capacitance would be the series combination of the free-space
capacitances of both plates, if you take them apart by a large distance.
The energy doesn't vanish. Actually, the stored energy is -increased-
when you take the plates apart, with the excess of energy coming
from the applied mechanical energy.

The initial energy is, as you say, E = 0.5*C*V^2 = 0.5*Q*V,
where Q is the charge in each plate (+Q in one plate, -Q in the other).
When you change the capacitance between the plates to C1, with Q
retained, the voltage changes to V1=V*C/C1 (because Q=C*V=C1*V1),
and the stored energy changes to E1 = 0.5*Q*V1 = 0.5*Q*V*C/C1 =
= E*C/C1.
If it were possible to decrease C1 to zero, the required energy
for this would be infinite! But in practice, it's never possible
to decrease C1 below the series association of the free-space
capacitances of the plates, and so the required energy to take
the plates apart, no matter to what distance, is finite.

When you decrease the distance between the plates again, you have
to apply a force to impede them to accelerate one against the
other. The energy spent on this (or the energy that can be taken
from the plates in this way) is the same that was added to the
system when the plates were taken apart.

These are the principles that make all the electrostatic
generators and motors work.

Antonio Carlos M. de Queiroz