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 6.6 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? -F 9

Explanation / Answer

let the charge initially on sphere 1 and sphere 2 be "Q"

force between the two charges is given as

F = k Q2/r2

6.6 = k Q2/r2 eq-1

after sphere 3 is touched with sphere 1,

Q3 = charge on sphere 3 = Q1' = charge on sphere 1 = Q/2

after sphere 3 is touched with sphere 2,

Q'3 = charge on sphere 3 = Q2' = charge on sphere 2 = Q3 + Q2/2 = ((Q/2) + Q)/2 = 0.75 Q

F' = force now acting on charge Q2 = k Q1' Q2' /r2 = k (Q/2) (0.75 Q) /r2 = (0.375) k Q2/r2

using eq-1

F' = (0.375) F = (0.375) (6.6) = 2.5 N

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