We all have seen experiments where an electric arc is created. Sometimes arcs of four inches are created with pretty rudimentary devices. When two electrodes are brought close together, a spark flashes. Then the arc is created an the experimenter moves the electrodes further apart. My question is about the distance between two electrodes. What exactly should the distance be for a spark to flash? How is it related to the voltage?
it depends on many things, assuming you are working with air there is a set number for breakdown at normal atmospheric pressure which is 3kV/mm
For breakdown on gases
atmospheric pressure will affect this(known as pashchen's law) humidity also will divert this value also remember this not a certain thing and usually the value given is for 50% chance of an arc happening.
Now the relation with voltage is mostly a limit of electric field that can be applied to the air before it becomes conductive.