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Q.

A charge ‘q’ is distributed over two concentric hollow conducting sphere of radii r and R (>r) such that their surface charge densites are equal. The potential at their common centre is

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a

Zero

b

q4π∈0(r+R)(r2+R2)2

c

q4π∈0[1r+1R]

d

q4π∈0[r+R(r2+R2)]

answer is D.

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Detailed Solution

Given (q−x)4πR2=x4πr2(q−x)=xR2r2q=x(R2+r2r2)x=q(r2R2+r2) ∴(q−x)=q(R2R2+r2)Common potential at centre=k[xr+q−xR]=14π∈0[r+RR2+r2]q

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