# Electric field due to a charged hollow spherical shell

A hollow spherical shell carries charge density p = k / r^2, in the region a<=r<=b. Find the electric field in i) the region a< r< b. ii) r> b
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I actually know how to find the E-Field, I'm having trouble with finding the enclosed charge.

For i) I found that the enclosed charge is Q_enc = 4pi.k(b-a), because I did a volume integral of the density, where I set phi to go from 0 to 2pi, theta to go from 0 to pi, and r to go from a to b. Since a<=r<=b, I said r goes from a to b. But the book says that r goes from a to r, and Q_enc = 4 pi. k (r-a)., which doesn't make any sense to me.

The book says that the integration variable of r' should go from a to r. If someone could specifically explain how they get the limits of integration on r', it would be much appreciated! Also, how would find the limits of integration for ii)r > b [for finding the enclosed charge?]

Solution Summary

This question talks about the Electric field due to a charged hollow spherical shell. The solution points out how to find the enclosed charge in various regions of the shell. Solution contains a clear diagram as well.

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Sithy Maharoof, PhD

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Active since 2012

PhD, Wayne State University

Responses 323

"Abit of upset as i thought the 1st attachment as in PV.gamma jpg could be a new approach but after saw the derivation you provided, both is the same thing. Thank you for providing such a clear answer."

"Thank you for your detailed explanation. Sorry for uploading the wrong file if it created any confusion."

"Thanks"

"Thank you. When I made the change in the problem I did not make the other changes. Thank you for clearing that up. I made it harder than it really was, thank you!! :))"

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