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Question

The region between two concentric spheres of radii 'a' and 'b', respectively (see figure), has volume charge density ρ=Ar, where A is a constant and r is the distance from the centre. At the centre of the spheres is a point charge Q. The value of A such that the electric field in the region between the spheres will be constant, is


A
Q2πa2
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B
Q2π(b2a2)
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C
2Qπ(a2b2)
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D
2Qπa2
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Solution

The correct option is A Q2πa2
Let us find total charge enclosed in a sphere of radius r,

Q=Q+raAr4πr2dr=Q+2πAr22πAa2

By Gauss law,
E×4πr2=Q2πAa2+2πAr2

Given, E is independent of r
Hence, Q2πAa2=0

This gives A=Q2πa2

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