Equation to relate voltage to distance of a spark

[professor]

I need to calculate the minimum distance for which a charge of some voltage will jump. Is there any equation that relates distance of a spark jump to voltage (a fairly generalised equation will do, I don't need to worry about strange shapes of the charged bodies that the charge leaps between or anything). Assume that this occurs in a vacuum. (This isn't homework, just part of a side project, and I am stuck because I can't figure out the above sub-problem, which hopefully isn't too difficult).

 

[bassplayer142]

You might want to start with this.

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

 

[astrokreng]

Yes, there is an equation that relates voltage to the distance of a spark jump. This equation is known as the Paschen's Law and it states that the minimum distance (d) for a spark to jump is inversely proportional to the product of the pressure (p) and the voltage (V) and directly proportional to the natural logarithm of the product of the pressure and the voltage. Mathematically, it can be expressed as:

d = a * (p * V) / ln(p * V)

where a is a constant that depends on the gas used and the shape of the electrodes.

In a vacuum, the pressure is close to zero, so the equation simplifies to:

d = a * V / ln(V)

This equation is fairly general and can be used to calculate the minimum distance for a spark to jump for different voltages in a vacuum. However, it is important to note that this equation is only valid for uniform electric fields and does not take into account the shape of the charged bodies or any other factors that may affect the spark jump distance. Therefore, it is recommended to use this equation as a starting point and make adjustments based on the specific conditions of the experiment.