If on the concentric hollow spheres of radii r and R(> r) the charge Q is distributed such that their surface densities are same then the potential at their common centre is
A
Q(R2+r2)4πϵ0(R+r)
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B
QRR+r
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C
Zero
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D
Q(R+r)4πϵ0(R2+r2)
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Solution
The correct option is DQ(R+r)4πϵ0(R2+r2) q1+q2=Q and q14πr2=q24πR2 (given) q1=Qr2R2+r2 and q2=QR2R2+r2 Potential at common centre 14πϵ0[Qr2(R2+r2)r+QR2(R2+r2)r]=Q(R+r)4πϵ0(R2+r2)