What is the Electrostatic Potential Energy of a Charged Spherical Conductor?

[clickcaptain]

Homework Statement

What is the electrostatic potential energy of an isolated spherical conductor of radius 24 cm that is charged to 3.9 kV?

Homework Equations

Electric potential

U = (kQ)/r

The Attempt at a Solution

U = ((8.99 * 10⁹ ) * (3.9 * 10³)/(0.24)

Could someone walk me through how to do this? Its a simple problem I know...but I'm not understanding it, thanks!

 

[LowlyPion]

You may be confusing kV with Coulombs here.

The Voltage is your electrostatic potential energy and is supplied by the kQ/R relationship.

But they didn't give you the charge on the sphere.

 

[clickcaptain]

The answer has to be formatted in Joules.. so its work, but I'm not exactly sure how to get work from an energy field.

 

[LowlyPion]

So then you're wanting to know how much work is required to charge a sphere?

So Work = V * q

As you bring the charges to the sphere, there will be work for each charge carried in from ∞. The average ΔV will be 1/2*V that the charges will need to be brought in against. That means for all the charges the total work will be 1/2*V*Q - where Q is the total charge.

But we also know that V = kQ/R, so rewriting we have

W = 1/2*V*(V*R/k) = 1/2V²*R/k

Or if you looked at it like a capacitor - a spherical one floating in space - then you can start from Q = V*C and since the potential energy in a capacitor is 1/2Q²/C you can rewrite that as 1/2*k*Q²/R = 1/2*V²R/k