# Static charge

i been watching some lectures from OCW and the professor said something like a ball with a radius of 1m can not exceed 3MV because of the electric breakdown of air.

to me it sounds like you can not exceed a potential difference 3MV per meter. so it does not matter the physical size of an object just the voltage difference over a distance is less.

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Andrew Mason
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i been watching some lectures from OCW and the professor said something like a ball with a radius of 1m can not exceed 3MV because of the electric breakdown of air.

to me it sounds like you can not exceed a potential difference 3MV per meter. so it does not matter the physical size of an object just the voltage difference over a distance is less.
It is the strength of the electric field, not the potential of the ball that determines when the air breaks down.

You can use Gauss' law to determine the electric field:

$$\int E\cdot dA = \frac{q}{\epsilon_0}$$

$$E = \frac{q}{4\pi r^2\epsilon_0}$$

The electric potential outside the sphere is the same as if you were dealing with a point charge:

$$V = \frac{q}{4\pi r\epsilon_0}$$

which means that E = V/r

So you can see that for a given voltage of a conducting sphere, the field strength varies as 1/r.

AM

http://en.wikipedia.org/wiki/Electrical_breakdown

Electrical breakdown occurs within a gas (or mixture of gases, such as air) when the dielectric strength of the gas(es) is exceeded. Regions of high electrical stress can cause nearby gas to partially ionize and begin conducting. This is done deliberately in low pressure discharges such as in fluorescent lights (see also Electrostatic Discharge) or in an electrostatic precipitator.

Partial electrical breakdown of the air causes the "fresh air" smell of ozone during thunderstorms or around high-voltage equipment. Although air is normally an excellent insulator, when stressed by a sufficiently high voltage (an electric field strength of about 3 x 106V/m[1]), air can begin to break down, becoming partially conductive. If the voltage is sufficiently high, complete electrical breakdown of the air will culminate in an electrical spark or arc that bridges the entire gap. While the small sparks generated by static electricity may barely be audible, larger sparks are often accompanied by a loud snap or bang. Lightning is an example of an immense spark that can be many miles long. The color of the spark depends upon the gases that make up the gaseous media.