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

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Homework Help Overview

The problem involves calculating the electrostatic potential energy of an isolated spherical conductor with a specified radius and voltage. The subject area pertains to electrostatics and energy concepts in physics.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to apply the formula for electrostatic potential energy but expresses confusion regarding the relationship between voltage and charge. Some participants question the need for the charge value and clarify the distinction between voltage and energy. Others suggest considering the work done in charging the sphere and provide alternative formulations involving work and potential energy.

Discussion Status

The discussion is active, with participants exploring different interpretations of the problem and offering insights into the relationships between voltage, charge, and work. There is no explicit consensus yet, but several lines of reasoning are being examined.

Contextual Notes

Participants note the absence of the charge value for the sphere, which is essential for calculations. Additionally, there is mention of the need to express the final answer in Joules, indicating a focus on energy units.

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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!
 
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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.
 
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.
 
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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