# How can two steel balls with same amount of charge be at different voltages?

Maybe this is the most fundamental question, but still it eludes me.

Is it possible for two balls each containing 1 Coulomb of charge be at different voltage levels, say 1V and 2V relative to a common ground?

Analogizing:

Mechanics as Electronics

Let,

Charge's mechanical equivalent is Mass
Voltage's mechanical equivalent is Potential energy
Current's mechanical equivalent is Fall (useful work can be done when a mass falls and also current flows)

In mechanics: For two bodies with same mass to be at different potential energy, all we have to do is vary the height from the ground.

So, what could be the Electrical equivalent of 'Height'?

• Your axioms themselves are fundamentally flawed. – Ignacio Vazquez-Abrams Aug 21 '14 at 4:06
• You said it yourself: Voltage = potential energy = height. – Dave Tweed Aug 21 '14 at 4:21
• @DaveTweed, you got me wrong, Potential energy alone is compared to Voltage. To vary the voltage of a ball having a constant charge, what should be change. Like in mechanics Height has to be changed to change potential energy(while having mass constant). I am asking the Electrical equivalent of 'Height' – user50716 Aug 21 '14 at 4:41
• @IgnacioVazquez-Abrams Thanks for saying that, but how it is wrong – user50716 Aug 21 '14 at 4:41
• I think your analogies are not correct. Voltage = Force and Energy = Energy – Plutonium smuggler Aug 21 '14 at 19:01

V = Q/C so if C is less, then V must be higher.

In this case, C is less if the ball is physically higher above a ground plane, and it takes energy to pull the ball higher, even in the absence of gravity.

• The other way is if the two balls have different radii. Capacitance of a sphere is ~4*piepsilon-sub zeroradius. (Assuming the ground reference is a long distance away >> radius.) Then the bigger sphere has more C. – George Herold Aug 21 '14 at 15:13
• @GeorgeHerold So if had a conductive balloon and charged it, then allowed it to deflate we should be able to trigger a spark if the spacing is right. – Spehro Pefhany Aug 21 '14 at 15:27
• Yeah I guess so... (in practice it's hard to keep charges on sphere's.) OK how about we pump the balloon up and down.. putting charge on when it's big and taking it off at a higher voltage when it's small. (wait for it..... it's a charge pump :^) – George Herold Aug 21 '14 at 15:34

http://lpsa.swarthmore.edu/Analogs/ElectricalMechanicalAnalogs.html

Firstly, as said, your axioms are flawed. Take a look at above link.

Capacitance -> Mass (although spring is mentioned, but its still near i guess, to explain without an inductor in the equation )

Voltage -> Force

Is a better anology.

By that rule, energy is stored in the Mass by applying a force and moving it against gravity through distance H.

Likewise, energy is stored in Capacitance by applying a voltage and pushing against already stored charge.

(I still dont see the anology of height though. Suggestions welcome)