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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SUMMARY

The discussion focuses on calculating the work done to construct a dielectric sphere with an offset hollow cavity using a work integral approach. The proposed formula is Work = integral dWork = integral delta V dq = integral delta V 4(pi r^2) dr. However, the challenge arises from the non-constant electric field E at a given radius r due to the offset cavity, raising questions about the feasibility of using a single integral for this calculation.

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Understanding of electrostatics and electric fields
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Knowledge of dielectric materials and their properties
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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.