# Spherical capacitors and their discharge rates?

Imagine that you have 2 small metal spheres (about $$2\mathrm{cm}$$ diameter), which are set $$x\mathrm{mm}$$'s apart from each other, with only air in between. You start to charge the spheres, one positively and one negatively, continuously.

After a while, you would expect to see a spark between the spheres, and the sparks would be seen periodically as the spheres are still loaded with charge.

How do you think that the period of discharge (sparks) would change as the distance $$x$$ between the spheres increases? ($$x$$ is in creased to the point that the spheres are no longer able to discharge.)

• What are your ideas and the reasons for them? – Farcher Sep 21 '17 at 18:14
• Its for an experiment – Skkk Sep 22 '17 at 7:35
• Then start with a prediction which relates the frequency of sparking if the charging is done continuously using a Van de Graaff generator, the "fatness" of the sparks to the separation of the spheres. – Farcher Sep 22 '17 at 11:19

In order to be able to answer the question, you have to know that air is a "dielectric" between the spheres, and it has a constant linear value, say 1kv/cm.
If you start with a gap of 1cm, there will be no spark until the spheres are charged to 1kv. Once it sparks (discharges), the voltage will drop and the arching stops. Since you have a generator that is supplying additional charge, the charge on the spheres will increase once more until the sparking voltage is reached, and the process repeats.
Assuming that the generator is capable of generating 10kv, then when you change the gap to 2cm, there will be no spark until the spheres are charged to 2kv. Once it sparks (discharges), the voltage drops... and the process repeats.
If you continue increasing the gap, you should notice that the interval between sparks (discharges) depends only on how quickly the generator charges the spheres to the required sparking voltage. In other words, it is the charging capability of the generator that determines the repeat interval, and it is the gap that determines at what voltage the spark will happen.