Electrostatics - probably a standard question

AI Thread Summary
The discussion revolves around calculating the total charge and electric field of a solid non-conducting sphere with a non-uniform charge distribution. The total charge is derived as Q = ∏ρsR^3 through integration. For the electric field inside the sphere, participants note the lack of symmetry and suggest that Gauss's theorem may not apply directly. However, it is recommended to find the charge enclosed within a radius r' < R and use integration to determine the electric field. The conversation highlights the need for careful consideration of charge distribution when applying electrostatic principles.
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Q) A solid non-conducting sphere of radius R carries non-uniform charge distribution with charge density ρ = ρs(r/R), where ρs is a constant. Show that
(a) the total charge on the sphere is Q = ∏ρsR3, and
(b) find the electric field inside the sphere.

Now first part (a) is fairly easy,
assumed a sphere of radius x and then after further integration got the result

But i need an idea for the second part..
since there is no symmetry so "Gauss" theorem is of no use applying...
I think i need an integration there as well. But can someone provide me an idea on how to continue further. Thanks in advance.
 
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since there is no symmetry so "Gauss" theorem is of no use applying...
There is a spherical symmetry.
 
How did you get the answer to part a. It seems incorrect to me.
 
Never mind, I got it.
 
barryj said:
Never mind, I got it.

what about the electric field?
 
exuberant.me said:
what about the electric field?

Use Gauss' theorem. Find the charge enclosed in a radius r'<R. Use integration.
 

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