spherical shell of inside radi. a and outside radi. b, ba,has a spherically symmetric volume charge densi.ρ(r)=k/r² for ab. a)Deter. the elec.field strength at arbitrary points inside and outside the shell using Gauss' law. b)Integrating the results of part a inward from infinity, find the poten. at an arbitrary point within the shell (a

Question

spherical shell of inside radi. a and outside radi. b, b>a,has a spherically symmetric volume charge densi.ρ(r)=k/r² for ab. a)Deter. the elec.field strength at arbitrary points inside and outside the shell using Gauss' law. b)Integrating the results of part a inward from infinity, find the poten. at an arbitrary point within the shell (a

goformit100 · Answer

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anonymous · Answer

Well.. to calculate the electric field at any point outside the shell is pretty easy.. so ll leave that up to you

Inside the shell is zero.. cause no charge is enclosed..

but at any random point p at a distance r from the centre such that   a<r<b.. |dw:1378621766515:dw|

apply Gauss law
$$ \int\limits_{}^{}\bar E.\bar {dA}= \frac{Q_{enc}}{\epsilon_0}$$

Due to symmetry.. the dot product vanishes, and you get E out.. and you can easily evaluate that trivial integral.. what now is Q_enc? 

well $$\sigma = \frac{dQ}{dv}$$

or $$Q = \int\limits \sigma dv$$

can u calculate further?!