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A charge 'Q' is distributed over two con...

A charge 'Q' is distributed over two concentric hollow spheres of radii 'r' and 'R' (gtr) such that the surface densities are equal. Find the potential at the common centre.

A

`(Q(R^(2)+r^(2)))/(4piepsilon_(0)(R+r))`

B

`(QR)/(R+r)`

C

Zero

D

`(Q(R+r))/(4piepsilon_(0)(R^(2)+r^(2)))`

Text Solution

Verified by Experts

The correct Answer is:
D
`q_(1)+q_(2)=Q and (q_(1))/(4pir^(2))=(q_(2))/(4piR^(2))`

`implies (q_(1))/(q_(2))=(r^(2))/(R^(2))`
`q_(1)+(q_(1)R^(2))/(r^(2))=Qimpliesq_(1)[(r^(2)+R^(2))/(r^(2))]=Q`
`implies q_(1)=(Qr^(2))/((r^(2)+R^(2)))`
Similarly, `q_(2)=(QR^(2))/((r^(2)+R^(2)))`
Potential at common center
`V=(1)/(4piepsilon_(0))[(q_(1))/(r)+(q_(2))/(R)]=(Q(R+r))/(4piepsilon_(0)(R^(2)+r^(2)))`.
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