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.

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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 Preview
(i) for a <= r <=b

Your approach is correct. Since this problem has spherical symmetry you only need to worry about the radial coordinate. Volume element is 4 pi r^2 dr.
You are asked to find the electric field at an arbitrary location between a and b. Lets find the E filed at …

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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.To continue with the answer check on mycoursewriter.com/

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