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Q.

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

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a

QRR+r

b

Zero

c

QR+r4π0R2+r2

d

QR2+r24π0R+r

answer is D.

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Detailed Solution

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 Let say charge q1 is on inner sphere and  charge q2 is on outer sphere  q1+q2=Q  and  q14πr2=q24πR2  (given) q1=Qr2R2+r2 and q2=QR2R2+r2 Potential at common centre=V=V1+V2 =14π0Qr2R2+r2r+QR2R2+r2R=QR+r4π0R2+r2Potential inside shell = potential on the shell

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