Charge Redistribution
Because a spark is an electrostatic effect, and does not
conduct a DC current, a return DC path to the source is not needed to support
it. See Exhibit
1a.
Exhibit 1: Charge Redistribution
Suppose a voltage V made by charge Q exists on capacitor
C1, and capacitor C2 is initially uncharged. There is no
energy stored in capacitor C2, so the total energy of the two
capacitors is the energy stored in capacitor C1, or QV/2. If the
switch is closed, the charge originally present on C1 is
redistributed between C1 and C2. Because Q = CV is
conserved, and the capacitance is now doubled to 2C, the voltage on the
capacitors is now halved, to V/2. The total energy stored in the two capacitors
is now Q(V/2)/2 = QV/4. Where did the energy go? The "missing" energy, QV/4, was
dissipated in the spark jumping the switch terminals as it closed.
The interesting point in this thought experiment is one that is
rarely mentioned; it is not necessary for the "bottom" plates of the capacitors
to be connected together, or to anything else, to see this effect, because it is
an electrostatic effect — a physical manifestation of charge redistribution. No
return path is needed because no direct return current exists—only the
displacement current associated with the capacitance between the two capacitors.
This is clear to those performing helicopter rescues on ships at sea;
triboelectric charging associated with the helicopter moving through the air can
result in a significant ESD event when the helicopter lowers its rescue basket to the deck of a ship,
especially in dry, fair weather. Sailors are told to let the basket touch the
deck first, before they touch it.
Perhaps a more intuitive (and in some ways, more physically
correct) view is to remove the ground completely as illustrated in Exhibit 1b, and
consider the ESD event to be the discharge of a single capacitance between two
objects, one of which is neutral and one of which has a mobile charge Q placed
on it. (Because charge is conserved, an object with a charge −Q on it exists somewhere in the universe, but this object
will be ignored.) Without loss of generality, one may assume the neutral device
as a reference; it is clear then that the only currents involved in the ESD
event are the current through the discharge itself, and the displacement current
through the electric field of the discharging capacitance.
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