Is Electric Flux Undefined with Surface Charges on a Sphere?

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SUMMARY

The discussion centers on the concept of electric flux in relation to surface charges on a sphere, specifically referencing the 1982 AP Physics C E&M Free Response question. The official solution states that electric flux through a closed surface is calculated as the charge enclosed divided by epsilon_0. However, a participant argues that the electric flux is undefined due to the presence of charges on the surface, leading to an infinite electric field at those points. The radius of the sphere is clarified to be 2a, which is crucial for understanding the problem.

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  • Understanding of electric flux and its mathematical definition
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  • Knowledge of electric fields and their behavior near surface charges
  • Basic concepts of integrals in physics
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This discussion is beneficial for physics students, educators preparing for AP Physics C, and anyone interested in advanced electromagnetism concepts, particularly regarding electric flux and surface charges.

lugita15
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Homework Statement


This was on the 1982 AP Physics C E&M Free Response
1982 Physics C Problem.JPG

Homework Equations


Electric flux through a closed surface = (Charge enclosed)/epsilon_0

The Attempt at a Solution


This is the official solution given:
1982 Physics C Solution.JPG

I believe, however, that the electric flux must be undefined. The electric flux is the integral of E.dA. But since there are charges *on* (as opposed to inside) two of the points on the sphere, E at those points would be infinite. Thus, integral E.dA would be undefined.

Any help would be greatly appreciated.
Thank You in Advance.
 
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I think you have misread the question. The radius of the sphere is 2a, not a.
 

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