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Two isolated conducting spheres of radii 0.02 m and 0.04 m are far…
Question
Two isolated conducting spheres of radii 0.02 m and 0.04 m are far apart. The smaller sphere carries a charge of 6 nC and the larger is initially uncharged. They are then connected by a long thin conducting wire and allowed to reach equilibrium. Find the final charge on the smaller (0.02 m) sphere, in nanocoulomb.
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Step-by-step solution
After connection the spheres reach a common potential.
For isolated spheres V = kq/r, so equality gives q1'/r1 = q2'/r2, hence q1'/q2' = r1/r2 = 0.02/0.04 = 1/2.
Charge is conserved: q1' + q2' = 6 nC.
With q1' = q2'/2, we get q2'/2 + q2' = 6, so q2' = 4 nC and q1' = 2 nC.
Final charge on the smaller sphere = 2 nC.
Final answer2
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