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miguzi

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A thick spherical shell of charge Q and uniform volume charge density p is bounded by radii r1 and r2, where r2 > r1. With V = 0 at infinity, find the electric potential V as a function of the distance r from the center of the distribution, considering the regions (a) r > r2, (b) r2 > r > r1

a) I got V = (kQ)/r

b) I found that p = 3Q/(4Pi(r2^3-r1^3))

using that I found that qencl = Q*(r^3-r1^3)/(r2^3-r1^3)

Then using Gauss' Law I found that E = Q/(4*PI*r^2*Eo) * ((r^3-r1^3)/(r2^3-r1^3))

Change in E potential = -integral(E)*dr lower limit r^2, upper limit r

Vr - Vr2 = -kQ/(r2^3-r1^3) * (r^2/2 - r1^3/r + r2^2/2 + r1^3/r2)

I'm stuck at this part

The answer is:

I don't how they simplified the answer to that

a) I got V = (kQ)/r

b) I found that p = 3Q/(4Pi(r2^3-r1^3))

using that I found that qencl = Q*(r^3-r1^3)/(r2^3-r1^3)

Then using Gauss' Law I found that E = Q/(4*PI*r^2*Eo) * ((r^3-r1^3)/(r2^3-r1^3))

Change in E potential = -integral(E)*dr lower limit r^2, upper limit r

Vr - Vr2 = -kQ/(r2^3-r1^3) * (r^2/2 - r1^3/r + r2^2/2 + r1^3/r2)

I'm stuck at this part

The answer is:

I don't how they simplified the answer to that

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