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 = 7.1 N. Suppose now that a third identical sphere 3, having an insulating handle and initially neutral is touched first to sphere 1 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 ? Number Units

Explanation / Answer

Let the Initial charge of both of the spheres be Q.

Let the separation of the charges be r.

Force between two spheres F = KQQ /r 2   

   KQQ /r 2 = 7.1 N --------------( 1)

Charge on sphere 1 and 3 after touched first sphere Q ' = (Q +0) / 2 = Q/2

Charge on sphere 2 and 3 after touched second sphere Q " = ( Q +Q') / 2 = (Q+0.5Q) /2 = 0.75 Q

The magnitude of the electrostatic force F ' that now acts on sphere2 is F ' = KQ'Q" /r 2

F ' = K(Q/2)(0.75Q) / r 2

= 0.375 KQQ/r 2

= 0.375 F Since from equation(1)

= 0.375 (7.1N)

= 2.6625 N

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