Potential and Current of Static Spark (Rug, Balloon)
Date: Winter 2011-2012
What is the potential (voltage) and current (amperage) on a static electric shock, say, from rubbing your feet on a dry carpet, or when you rub a balloon on your hair and then touch someone?
This kind of thing is routinely estimated by electronic engineers
worrying about ESD (ElectroStatic Discharge) damaging their products.
The voltage attained varies so easily you cannot predict the value from the charging method.
To know, one uses a method, then measures the actual potential of the body with respect to ground
using specialized meters optimized for measuring static voltages or fields.
I see one at : http://search.digikey.com/us/en/products/718/SCP294-ND/555891 .
But, for walking across carpet, the range is from 500v to maybe 30,000v.
50,000 volts is conceivable.
10,000 volts would be a common easily attained level.
The standard "Human Body Model" represents a typical body over a conductive floor as
a 100pF (picoFarads) capacitor plus a 1500 ohm resistor in series.
Both can vary substantially, but those are considered standards.
I tend to use 300pF and 1000 ohms to be more conservative.
So, for a 300pF human body model charged to 30,000v:
Peak Current is estimated: I = V/R = 30,000 volts / 1000 ohms = 30 amps. (Not really sky-high!)
I think measured values have been shown at about 80A.
Charge Q = C * V = 3e-10 Farad * 3e4 volt = 1e-5 Coulomb = 10 micro-amp.seconds..
Pulse Duration (presuming it's square, but it's really more like exponential-decay)
t = Q / I = 1e-5 coulomb / 30 amp = 0.3 microsecond = 300nsec.
Discharge Energy E = V^2 * C / 2 = (3e4)^2 * 3e-10 / 2 = 0.15 Joules.
Peak Power = Energy / Duration or PeakCurrent * ChargeVoltage
= 30 Amps * 30,000 Volts = 1 mega-Watt (that part is kinda big!)
Most of the energy and power is probably dissipated in the skin-resistance of the person discharging to ground,
not in the spark, because the spark tends to have resistance much lower than 1000 ohms, once started.
There is a rough proportionality between sparkover distance and the charge voltage,
but it's anecdotal and I don't remember the typical factor.
Below about 2000v one usually can't feel or hear the discharge from a human body's small capacitance.
Rubbing a balloon on hair creates a good density of charges on the balloon,
the equal-and-opposite charge on the body spreads out over the whole body
and probably doesn't charge the body to more than 5kv with respect to the conductive ground beneath your feet..
Reaching a high voltage that way would require rubbing with several balloons in sequence,
or re-using the same balloon several times after discharging it's surface to ground each time.
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Update: June 2012