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 (see Figure (a)). The magnitude of the electrostatic force acting on sphere 2 due to sphere 1 is F = 9.1 N. Suppose now that a third identical sphere 3, having an insulating handle and initially neutral, is touched first to sphere 1 (see Figure (b)), then to sphere 2 (see Figure (c)), and finally removed (see Figure (d)). What is the magnitude of the electrostatic force F' that now acts on sphere 2?

Explanation / Answer

From Coulomb's Law we have F = k*q^2/r^2

Now when the third sphere is touched to the first q1 is now q/2 and q3 = q/2

Now when it is touched to the 2nd sphere its charge becomes 0.75q

So F' is now 0.5q*0.75q/r^2 = 0.375q^2/r^2

So F' = 0.375*F = 0.375*9.1N = 3.4 N....Ans.

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