Two identical conducting spheres each having a radius of 0.5 cm are connected by a light
2 m long conducting wire. A charge of 60 µC is placed on one of the conductors. Assume that the surface distribution of charge on each sphere is uniform. Determine the tension in the wire. In Newton’s.

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answer is 2.

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Detailed Solution

The charge divides equally between the identical spheres, with charge Q/2 on each. Then they repel like point charges at their centers so, we have
$F = \frac{1}{4 π \in_{0}} \frac{(\frac{Q}{2}) (\frac{Q}{2})}{{(L + R + R)}^{2}} = \frac{1}{4 π \in_{0}} \frac{Q^{2}}{4 {(L + 2 R)}^{2}}$
$F = \frac{9 \times 10^{9} \times {(60 \times 10^{- 6})}^{2}}{2} ≅ 2 N$