(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Right have a shell that has a volym charge distribution P=(G/r^2) and with inner radius a and outer radius b.

Now what is the e-field at r<a, a<r<b, r>b

2. Relevant equations

gauss's law: surfaceint[E.da]=Qenclosed/epsilon0

Qenc=volymint[PdV)

3. The attempt at a solution

Right this is what i tried.

for r<a: there is no enclosed charge so E is zero at all points.

for a<r<b:

well first E is radially outwards and normal to the surface so the gauss integral just go to

E4[pi]r^2

Qenclosed=volymint[PdV] between r and a

goes to -> volymint[(G/r^2)(4[pi]r^2)dr] -> 4[pi]G*volymint[dr] evulated at r and a

-> 4[pi]G(r-a)

and E4[pi]r^2=(4[pi]G(r-a))/epsilon0

which then goes to -> E=(G(r-a))/(epsilon0*r^2)

then for r>b:

it's the same calc as for a<r<b but we end up with E=(G(b-a))/(epsilon0*r^2)

now i'm wondering have I done something wrong and if I had to plot it on a graph where we have E/r then for the first part upto a E would be zero and for the part where r>b it would follow a 1/r^2 relation, but how do i figure out the realation for part a<r<b, my algebra seems to suck a bit.. =)

but yeah.. does this look correct?

and if so, can you help me or give me a hint hwo to work out the relation.

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# E-field of non-conducting, nonuniform shell

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