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"Static Electricity" means "High Voltage"
Measuring your body-voltage

1999 William J. Beaty, BSEE

"Static electricity" is not electricity which is static and unmoving. Neither is it a form of energy.

Actually, the thing we call Static electricity is an imbalance. It's an imbalance in the amounts of positive and negative charges found within the surface of an object. Only the imbalance between opposite charges is important, and their motion or "static-ness" is irrelevant. For example, the imbalance can flow along as an electric current, yet it loses none of its familiar "static electrical" properties. While it is flowing the charge still crackles, glows, and attracts dust and lint. But how can we have "static" electricity that flows? Motionless motion? Simple. "Static electricity" is all about the charge-imbalance, and it has nothing to do with charges at rest. "Static electricity" was misnamed.

OK, then what exactly is "static" electricity? Here's a big clue. There's always a strong e-field (electric field) surrounding these charges, whether the charges are moving or still. This strong field is the main feature of so-called "static" electricity. But what's an e-field? One way to say it: an e-field is like a magnetic field, but it's electrical in nature. Another simple answer: an electric field is a voltage without a current. Whenever you have pure voltage, then you have a pure electric field with no magnetism involved: you have "electrostatics" without "magneto-statics."

Here's still another way to say it:
"Static Electricity" is not unmoving, it really means "High-voltage Electricity."

That's the answer. Static electricity is simply high voltage. High voltage has all the characteristics of "static electricity." And when grade-school textbooks are trying to teach us about "static," they are really trying to teach us about pure voltage: voltage without current.

When we scuff our shoes upon a rug on a dry winter day, our bodies typically charge up to a potential of several thousand volts with respect to the ground. This is a well-known fact in physics, and is easily verified by meter measurements. Touch a grounded object, and a spark will leap between the object and your fingertip. This type of long electric spark can only exist when a high voltage is present. The shortest, tiniest spark requires about 500 volts. Big, nasty, painful sparks require lots more voltage, up to several thousand volts. But even when no sparks are jumping, there's still a high voltage between your charged body and the ground. Your charged body is surrounded with an invisible electric field.

During low-humidity weather, scuffing of shoes upon rugs can put a huge voltage on your body. It is fairly easy to detect this voltage (try RIDICULOUSLY SENSTIVE CHARGE DETECTOR) However, this voltage is fairly difficult for students to measure. A normal voltmeter won't work: the electrical resistance of a normal voltmeter will discharge your body almost instantly (it places a 10-megohm resistor across a 200pF body capacitance, and by T=RC we calculate that the meter's resistor drains out your body's stored energy in two thousandths of a second.)

Recently I discovered that some teachers DON'T BELIEVE that "Static Electricity" actually involves high voltage. OK, then we need a simple way to prove it. Below are various ways to measure the high voltages which arise because of "static electricity" upon your body. Don't take my word for it, go measure it for yourself.

WAYS TO MEASURE "STATIC" HIGH VOLTAGES

  1. Electrometer, a zero-current voltmeter
  2. Length of a spark (small between large spheres)
  3. spark PAIN!, doorknob zaps
  4. Moving voltmeter, crude and simple
  5. "Field mill"
  6. Array electrometer
  7. Misc.
  8. Also see: HV polarity
  9. "Static" sparks: kilo-amperes and megawatts






1. Electrometer
This is the expensive way to do it. Obtain a professional electrometer or Electrostatic Voltmeter. The input resistance of the meter needs to be around a hundred billion ohms (10^11 ohms) or greater. Connect one meter terminal to ground, hold the other meter lead in your hand, scuff on the rug, and watch the voltage-reading on the meter as it climbs up to several thousand volts. (Humidity must be low, of course, or the rug-scuffing won't charge up your body.) To REALLY make the voltage go up, leap into the air while touching the meter's lead wire.

Electrometer Sources:

Or, try building one yourself:
Richard Hull's Electrometer schematic

2. Spark Length
To measure high voltage, attach two large and polished brass balls (2" dia. or larger) to an insulating plate so there is a 1/2 millimeter gap between them. You can verify the 2,800-volt breakdown voltage of this spark gap by using a high-voltage DC power supply to produce sparks between the balls. Now disconnect the power supply, ground one brass ball, hold your finger against the other one, and start madly scuffing your shoes on the rug. Sparks leap across the gap. Your body charges up to 3 kilovolts, and causes a spark-gap breakdown, just like the power supply did. (I've done variations on this measurement technique many times, since it makes an expensive electrometer unnecessary.) Sometimes, when humidity is extremely low and the rug is totally dry, you can widen the gap spacing by quite a bit, which implies that human body voltage exceeds 2,800 volts by quite a bit. Hint: rather than using large and expensive brass spheres, use two stainless steel mixing bowls. Mount them on some sort of plastic insulators so the round bottoms face each other across the tiny gap.

Info on spark gaps from Jim Lux:   Gap between
60mm spheres
0.5mm   
1mm  
2mm  
3mm  
4mm  
5mm  


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-
-
-
-
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volts
2850
4350
7350
10350
13350
16350


3. Doorknob spark, relative pain
Use an adjustable, calibrated High Voltage DC power supply to charge your body to various voltages ( EXTREME DANGER! Limit the current to below a few hundred uA by using a series resistor chain. If you don't know how to use DC high-volt power supplies safely, then don't mess with them. IF YOU DO THIS WRONG, IT CAN KILL YOU.) Use the power supply to charge yourself to 3KV, 5KV, 7KV, and touch a grounded knob each time. No electrometer is needed, yet you've just verified the length, sound, and pain-level of the fingertip spark which appears when your body had been forced to take on certain high voltages. This procedure is a great way to learn the types of sparks produced by various voltages on your body, so the next time you get zapped by a car-door, you can say "YOW!, the ouchiness-factor of that spark indicates a human body voltage on the order of seven kilovolts." :)

4. Hand-waving AC field magnitude
Crudely measure your body-voltage by using an oscilloscope to compare it to a high-voltage power supply. First, connect an oscilloscope's input to a metal plate. Scuff on a carpet (during a low-humidity day), wave your hand near the metal plate, and see how much the trace on the oscilloscope is deflected. Adjust the scope's vertical gain to give a fairly large deflection during your hand-waving. (Don't TOUCH the plate while your body is charged, or you might blow out the input amplifier on the scope!)

Next, use a DC high-voltage power supply with a large current-limiting series resistor to charge your body to 5,000 volts. ( EXTREME DANGER! You MUST limit the current to below a few hundred microamps by using a series resistor chain. If you don't know how to handle high-volt DC power supplies safely, then don't mess with them. IF YOU DO THIS WRONG, IT CAN KILL YOU.) Wave your charged hand near the metal plate while seeing how far the oscilloscope trace deflects. Adjust the HV supply voltage until the deflection is about the same as when your body was charged by the rug-scuffing. Read the power-supply voltage setting, and you will know the approximate body-voltage produced by rug-scuffing.


5. Crude and simple "field mill"
A more precise version of no. 4 above... Build a crude "field-mill" e-field sensor. TO do this, first use a small DC motor to whirl a grounded wire, then place an oscilloscope probe behind the whirling wire so it is alternately shielded and unshielded, mount the entire assembly an inch or so from a large, electrically floating brass ball, then observe the scope trace. The observed AC voltage will be proportional to any DC voltage on the isolated brass ball with respect to ground. Apply a known kilovoltage to the brass ball in order to calibrate it against the AC reading on the scope (for example, 1,000 volts applied to the brass ball will produce a certain AC voltage reading on the scope, and any other voltage applied to the brass ball will be proportional.) Now go scuff on a rug while keeping one finger on the brass ball, and see what voltage is detected by the system. (No oscilloscope? Try placing a small metal disk behind the whirling wire, then connect a digital voltmeter to the plate and to ground, then set the meter to a sensitive scale on AC volts. Calibrate the voltage reading on the meter against a known DC high voltage applied to the brass ball.)

To measure REALLY high voltages (such as those produced by a VandeGraaff machine), you can use the above technique, but use the VDG sphere itself instead of the "brass ball", and place the field-mill and the oscilloscope several feet away from the VDG sphere. Calibrate it as before. If 1KV applied artificially to the VDG sphere produces a certain waveform voltage, then 100KV will produce exactly 100 times higher AC voltage.


6. Electrometer Array
Build 300 crude electrometers which drive individual LEDs. Use them to build a "visible e-field detector panel." When charged objects approach the panel, the glowing field of LEDs darkens in a pattern around the object. Scuff on the rug, hold a hand up, and observe the darkened field around your hand. What body voltage does this imply? To find out, go grab the old 7KV supply, hold the live terminal, then wave your hand around the sensor panel. Whoa! The darkened field is larger than before. Decide that the rug-scuffing body-voltage must have been maybe half of the body voltage created by the 7KV supply, maybe 3,500 volts.




OTHER WAYS TO VERIFY THAT "STATIC ELECTRICITY" INVOLVES HIGH VOLTAGE

Read books which say that common "static electric" sparks first appear when the voltage on your body rises above 500VDC. Use a HV DC power supply to test this, and find that their estimate is too low, that sparks cannot be seen at all until 750V, and they are very hard to notice until the voltage on your body is above 1KV.

Calculate what happens when a charged balloon is lifted from your arm. Obtain a value of 100KV. Sounds sensible. Ordinarily a VandeGraaff Generator would be needed to make arm-hair stand up so fiercely.

Read research papers from people who measure such things. Here's one from J. Chubb Inc:
The Control of Body Voltage Getting Out of a Car      Their measurements for different clothing and various car-seats give impressively high voltages, and this occurred at humidity levels above 50%. The voltages should be MUCH higher at, say 5% R.H.!
  • Nylon clothes: 21,000 volts (Yowch!)
  • Wool clothes: 9,000 volts
  • Cotton clothes: 7,000 volts

Here's a suggestion taken from the PHYS-L discussion group:

Touch the electrode of a foil-leaf electroscope, and simultaneously scuff on the carpet. Observe the deflection of the foils. Now connect the electroscope terminal to an adjustable HV DC power supply with the other HV supply terminal connected to ground, and adjust the voltage to duplicate the foil deflection from before. Read the voltage. The power-supply voltage is the same as your rug-scuffing body-voltage was.





RUBBED-BALLOON VOLTAGE CALCULATION

I rub a balloon upon my arm hair. If I know the attraction force and the capacitance between those flat, plate-like regions of opposite charge, then I can calculate the voltage. If the attraction force is 0.1Nt (like a 10gram weight) and if it is independent of plate-separation (because the plates are closely spaced,) and if the spacing of the "capacitor plates" is initially 1mm (0.001meter), then it took an amount of energy equalling (Force*distance) to pull the attractive plates apart to 1mm, and the stored energy is:

Work = force * distance
.1Nt * .001meter = 1e-4 Joules. For the given attractive force between the plates, we see that 100 microjoules of electrical energy is stored by this capacitor.

OK so far? Now, what is the capacitance of two capacitor plates spaced 1mm apart and having the size of that typical contact area between the balloon and my forearm? Let's say the area is 4cm by 15cm, or .04*.15 = .006 square meters. The equation for calculating the capacitance of parallel plate capacitors (plates spaced very close) is

C = k * A/D

Capacitance = k*area / distance between plates, where the dielectric constant of air is k=8.9e-12 and the lengths are in meters, so the capacitance of the balloon/arm capacitor at a 1mm gap is 53pf.

An actual 4cm x 15cm foil-plate capacitor with a paper-stack dielectric measures 95pf on my capacitor meter, which is in the ballpark. We should expect it to be higher than our 53pF above, since it has a paper dielectric, not air.

The energy stored was 100 microjoules, so the voltage can be had from the equation for stored energy in capacitors:

U = 0.5 * C * V^2

Energy equals one half times capacitance times voltage squared, or Voltage=sqrt(2*U/C) (U is the stored energy.) Plugging in 100 microjoules and 53 pf I get an answer of 1900 volts. At 1mm spacing, the voltage is already almost 2,000 volts!

I also get a total charge of each imbalanced region which calculates to be about 0.1 microcoulomb:

U = 0.5 * Q^2 / C

U = F * d

Q = sqrt(2*C*F*d)

Force * distance = 1/2Q^2/C, or Q = sqrt(2CFd) = 1e-7coulombs. Capacitor voltage is always V = Q/C, and capacitance varies inversely with plate-spacing, therefor voltage varies directly with plate spacing. Double the plate spacing of charged, insulated plates, and we double the voltage.

   plate spacing  V(capacitor)
     1mm             1920v
     5mm             9600v      V = (1e-7)*D/(.006)/(8.9e-12)
     1cm            19200v
     5cm            95800v

WHOA! 100,000 volts at a couple of inches spacing?!! However, this is reasonable, since it normally takes a VandeGraaff Generator to make arm-hair stand up so painfully rigid. In the gap between the balloon and my arm-hair, we have electric field strength which is easily the same as the field strength at the surface of the sphere of a VDG machine. Also, the capacitor equation stops working correctly as we exceed about 1cm, when the plate spacing becomes large in comparison to the shortest side of each plate. Maybe the voltage at 5cm is really only 50,000 volts. Only!!!!!!!

The capacitor voltage varies as the square-root of the attraction force, so what would happen if this force was smaller? If the attraction between my arm and the balloon was only 0.01Nt (1 gram weight), then the voltage would start at 606V at 1mm, and go up to 6060V at 1cm. Not as huge, but still pretty impressive.

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