Electric Potentials: concentric spheres

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Homework Help Overview

The discussion revolves around the energy stored in a system of two concentric spheres with equal but opposite charges. The problem involves concepts from electrostatics, specifically related to electric potentials and capacitance of spherical shells.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to apply the relationship between potential energy and charge but expresses confusion about the setup and the nature of the spheres. They question whether the spheres are hollow and how to approach the problem mathematically.
  • Some participants suggest considering the capacitance of a spherical capacitor and refer to potential differences between the spheres as a possible avenue for solving the problem.
  • Others express uncertainty about their calculations and seek confirmation of their results, indicating a struggle with the underlying concepts.

Discussion Status

Participants are exploring various interpretations of the problem and discussing relevant formulas. There is a recognition of the complexity of the topic, and while some guidance has been offered regarding capacitance, there is no explicit consensus on the correct approach or solution.

Contextual Notes

The original poster mentions a time constraint due to an upcoming test, which may influence their ability to derive necessary formulas or fully understand the concepts involved. There is also a reference to potential confusion regarding the nature of the spheres being solid or hollow.

vsage
Two concentric spheres of radii 1.65 cm and 19.0 cm, respectively, are given equal but opposite charges of 6.35e-08 C. How much energy is stored in the system (in J)?

I know V = U/q where U would be the entire energy stored in the system beacuse it's not in motion. I know q's but I just don't know how to apply it.

I've thought about this so much. I tried setting up a ridiculous integral for solving this but it just went way over my head. The question doesn't really even make sense because wouldn't some of the charges overlap each other? I think the teacher meant hollow spheres. A little point in the right direction, please. (Test tomorrow) :)
 
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I think the problem is about spherical shells.

I'm curious - has your class discussed the capacitance of a spherical capacitor? If so then you may already have a formula for finding the energy stored. If not, nevermind! :-)
 
Yes the teacher touched on it for the last half of a lecture I think but it wasn't much more than parallel plates (a lecture is 2.5 hours though so that's a lot of time). Oh yeah I see it may be addressed in the chapter he touched on. Thanks tide I'll see if I can't work something out from this.

Ah, found it.

the potential difference between the spheres

q/(4*pi*enot) * (outer radius - inner radius) / (outer radius * inner radius)

I wish I had enough time to derive this formula but I'm in a crunch :\

My grasp of this subject is worse than I'd like it to be but since dV = dU/q ,
the total energy is dV * q? Am I correct?

Edit: The computer that checks my answers says I was wrong.. I got 4.98e11 joules
 
Last edited by a moderator:
Can my answer be confirmed? The computer keeps telling me I'm wrong argh. Ok now I'm getting 2e-03 joules which I know has to be wrong as well. This is so confusing sigh. Edit ok here my work:

C = q^2 / U

C = 4*pi*enot * (Ro * Ri) / (Ro - Ri)

where enot is 8.85e-12 and Ro is the outer radius and Ri is the inner radius

C = (6.35e-08)^2 / U = 2.01e-12

U = (6.35e-08)^2 / 2.01e-12

= 2.01e-03

:\
 
Last edited by a moderator:

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