Charge is distributed non-uniformly in the volume of a solid insulating sphere of radius 'a' such that volume charge density (ρ) varies with distance from the centre (r) as ρ (r) = Cr2, r ≤ a here C is a constant. Magnitude of electric field strength outside the sphere, i.e., for r > a, is :
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a
Ca55e0r2
b
Cr35e0
c
Cr22e0
d
Ca3e0r2
answer is A.
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Detailed Solution
Total charge Q = ∫ρdv=∫Cr2(4πr2dr)=4πC∫0qr4dr=4πCa55Electric field = Q4πe0r2=Ca55e0r2