Identical isolated conducting spheres 1 and 2 have equal charges and are separat

Question

Identical isolated conducting spheres 1 and 2 have equal charges and are separated by a distance that is large compared with their diameters (Fig. 21-22a).middotThe electrostatic force acting on sphere 2 due to sphere 1 is F. Suppose now that a third-identical sphere 3, having an insulating handle and initially neutral, is touched first to sphere 1 (Fig. 21-22b), then to sphere 2 (Fig. 21-22c), and finally removed (Fig. 21-22d). The electrostatic force that now acts on sphere 2 has magnitude F'. What is the ratio F'/F?

Explanation / Answer

F = k q q / r^2

F = k q^2 / r^2

when 3 is touched to 1 and removed then

q1 = q3 = (q + 0) / 2 = 0.5q

now q3 is touched to q2 and removed ,

q2 = q3 = (q + 0.5q)/2 = 0.75q

now F' = k (0.5q)(0.75q) / r^2

F' = 0.375 k q^2 / r^2

F' / F = 0.375 ...........Ans

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