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Electrostatic Potential Energy

by clickcaptain
Tags: electrostatic, energy, potential
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clickcaptain
#1
Feb9-09, 12:25 PM
P: 32
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!
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LowlyPion
#2
Feb9-09, 12:35 PM
HW Helper
P: 5,341
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
#3
Feb9-09, 12:38 PM
P: 32
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
#4
Feb9-09, 02:30 PM
HW Helper
P: 5,341
Electrostatic Potential Energy

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


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