Energy and Capacitors of metal spheres

[Mitchtwitchita]

Homework Statement

Two uncharged metal spheres, spaced 15.0 cm apart , have a capacitance of 24.0 pF. How much work would it take to move 12.0 nC of charge from one sphere to the other?

Homework Equations

V = Q/[4(pi)eor]
(delta)K + (delta)U = 0 *I think

The Attempt at a Solution

I'm not quite sure how to do this problem. I think I would first have to find out the potential difference between the spheres?

V = Q/[4(pi)eo*r]
=(12.0 x 10^-9)/[4(pi)(8.85 x 10^-12)(1.5 x 10^-1)
=719 V

Can somebody please tell me if I'm going in the right direction and, if not, could you please steer me in the right direction?

 

[hikaru1221]

From the law of energy conservation, the work needed = the change in the energy of the capacitor. So all you need to find is the initial energy and the final energy.

 

[Mitchtwitchita]

So, U = Q^2/2C would be the equation to use?

 

[hikaru1221]

Yes :)

 

[Mitchtwitchita]

Would the initial energy be 0 because they are originally uncharged?

 

[hikaru1221]

What do you think? :)

 

[Mitchtwitchita]

I think so because the electric field depends on the charge of the spheres. Therefore, if there is no charge, there can't be any electric field.

 

[hikaru1221]

There you go :)

 

[Mitchtwitchita]

Why is the distance given?

 

[hikaru1221]

It's redundant.

 

[Mitchtwitchita]

Oh, ok. Thanks for your time.