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Two metal spheres of radius r have cente...

Two metal spheres of radius r have centers at a distance d apart in air. Find the capacitance of the system.

Text Solution

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Consider the potential at a point p due to charge `+qand-q` on the two sphere `DeltaV=V_(1)-V_(2)`
`=(q)/(4piin_(0))[(1)/(r)-(1)/((d-r))]-((-q))/(4piin_(0))[(1)/(r)-(1)/((d-r))]`
`=(q)/(4piin_(0))[(2)/(r)-(2)/(d-r)]=(2q)/(4piin_(0))((d-2r)/(r(d-r)))`
Capacitance, `C=(q)/(Deltav)=(2piin_(0)r(d-r))/((d-2r))`
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