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Electrostatic Potential Energy 
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#1
Feb909, 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 * 10^{9} ) * (3.9 * 10^{3})/(0.24) Could someone walk me through how to do this? Its a simple problem I know...but i'm not understanding it, thanks! 


#2
Feb909, 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. 


#3
Feb909, 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.



#4
Feb909, 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) = 1/2V^{2}*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 1/2Q^{2}/C you can rewrite that as 1/2*k*Q^{2}/R = 1/2*V^{2}R/k 


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