Work done to construct Dielectric Sphere with Offset Hollow Cavity?

Thread starter TwoAyoyoprogrammer
Start date May 19, 2024
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Dielectric Sphere

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The discussion focuses on calculating work done in constructing a dielectric sphere with an offset hollow cavity using a work integral approach. The proposed formula involves integrating the product of voltage and charge over the sphere's surface area. However, the challenge arises from the non-constant electric field at a given radius due to the cavity's offset. Participants express the need for a visual representation to better understand the geometry and electric field variations. A sketch could significantly aid in clarifying the complexities involved in the calculations.

May 19, 2024

TwoAyoyoprogrammer

Homework Statement: Find the work done to assemble positively charged particles from infinitely far way, to create a uniformly charged dielectric sphere with charge +Q and radius R. There is an offset hollow cavity with radius R/2, and electrically neutral (no charge).

Relevant Equations: Work = integral dWork

My thinking would be to do a work integral
Work = integral dWork
= integral delta V dq
= integral delta V 4(pi r^2) dr

The problem is, is this possible with a single integral?
Due to the offset cavity, the electric field E will not be constant at a given r.

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Sep 2, 2024

Alex Schaller

A picture is worth a thousand words... Would you sketch such a picture?

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