Electrostatic Potential Energy

clickcaptain

1. The problem statement, all variables and given/known data

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


2. Relevant equations

Electric potential

U = (kQ)/r



3. 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