Work done to construct Dielectric Sphere with Offset Hollow Cavity?

In summary, the project involved the construction of a dielectric sphere featuring an offset hollow cavity. The primary focus was on the precise design and engineering of the sphere to optimize its dielectric properties while ensuring the cavity's offset enhances functionality. Various materials and methods were explored to achieve the desired structural integrity and electrical performance, leading to successful fabrication and testing of the sphere.
  • #1
TwoAyoyoprogrammer
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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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  • #2
A picture is worth a thousand words... Would you sketch such a picture?
 
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