    Question

# Two metal spheres (radii r1,r2 with r1<r2) are very far apart but are connected by a thin wire. If their combined charge is Q, then what is their common potential?

A
kQ/(r1+r2)
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B
kQ/(r1r2)
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C
kQ/(r1+r2)
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D
kQ/r1r2
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Solution

## The correct option is C kQ/(r1+r2)Potential due to a sphere of radius r having charge q is given by V=kqrLet the charge of the spheres be q1 and q2.After connecting both spheres, potential of both of them must be equal.Vc=V1=V2 ∴ Vc=kq1r1=kq2r2Thus we get q1q2=r1r2 .......... (i)Total charge remains constant so,q1+q2=Q ....... (ii)From Eqs. (i) and (ii), we get q1+r2r1q1=Q⟹q1=Qr1r1+r2Thus common potential Vc=kq1r1⟹Vc=kQr1+r2  Suggest Corrections  0      Similar questions  Related Videos   Electric Potential Due to Uniformly Charged Spherical Shell or Solid Sphere
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