Yahoo Answers: Answers and Comments for A solid nonconducting sphere of radius R carries a nonuniform charge distribution with charge density? [Physics]
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From Vignesh Y
enUS
Mon, 13 Apr 2009 09:30:55 +0000
3
Yahoo Answers: Answers and Comments for A solid nonconducting sphere of radius R carries a nonuniform charge distribution with charge density? [Physics]
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https://answers.yahoo.com/question/index?qid=20090413093055AADPaEh
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From Prashant: a)
The charge per unit volume is ρ=ρ1 (r/R)...
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https://answers.yahoo.com/question/index?qid=20090413093055AADPaEh
Mon, 13 Apr 2009 21:50:58 +0000
a)
The charge per unit volume is ρ=ρ1 (r/R) where r is the distance from the center.
Divide the entire sphere into infinite concentric spherical shells of thickness dr.
Consider one such shell with radius r.
So
volume of the spherical shell = 4πr^2 dr
Amount of charge on this shell
dq = volume*charge density = 4πr^2 ρ1 (r/R) dr
Integrate from r = 0 to r = R:
Q = π(ρ1)(R^3)
b)
Let the electric field at a distance r from the center be E.
Consider a Gaussian Surface t o be a sphere of radius r.
Charge enclosed by the surface can be calculated as in a. Integrate from r = 0 to r = r.
q = π(ρ1)(r^4) / R
Consider a small area element ds on the surface.
E and ds are parallel everywhere.
So
E.ds = Eds
d(phi) = Eds
Integrate :
Phi = EA = E (4πr^2)
(Integral of ds is the surface area of the sphere.)
From Gauss's Law :
q = Phi * ε_o
or
E = ρ1 r^2 / (4 R ε_o)
Substitute ρ1 = Q / (πR^3) from a.
E = (Qr^2)/(4πε_o R^4 )
Hope this helps.
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From gilfillan: Non Uniform Charge Density
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https://answers.yahoo.com/question/index?qid=20090413093055AADPaEh
Thu, 19 Jan 2017 15:57:16 +0000
Non Uniform Charge Density