General question - how much current is in a simple spark?

[elegysix]

All things being given - separation, breakdown V, temperature, and so on... If I have two pins and they are both connected to a high voltage capacitor & switch - (supposing the circuit has zero resistance aside from the separation and air)

How much current will flow in the spark which arcs between them?
(smooth surfaces if the shape of the pin is going to play into it... keep it simple for now)

two cases: one where the voltage is the bare minimum to breakdown the air, and another with excessive voltage.



--what would dβ/dt be? (can i use biot-savart ?) if I had a cleverly designed coil, so as to capture all of the magnetic flux from the current, would the current in the spark depend on the inductance of the coil?

 

[chrisbaird]

Actually, some of the most important factors are ones you seem to have missed or downplayed: humidity and electrode shape. Sharps points will arc more than flat surfaces because they create stronger fields locally. In fact, charge tends to leak off sharp points before it builds up enough to create visible arcing (depending on the voltage).

 

[elegysix]

I'd heard a little about that, that's why I mentioned it... I mean ... if we had two spheres and we knew the separation and voltage, and temp/humidity, is there a formula for an approximation to the current? anything? where do I start with this?