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 = 0.69 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

let the initial charge on 1 and 2 is q

and their seperation is given as d

F = k*q^2/d^2

k*q^2/d^2 = 0.69 -----(1)

when 1 and 3 are

q1 = q3 = q/2

Now, when q3 and q3 are touched

q2 = (q/2 + q)/2

q2 = 0.75 * q

Now ,New force = k * q1*q2/d^2

New force = k * (q/2) *(0.75 q)/d^2

New force = 0.375 * k*q^2/d^2

New force = 0.375 * 0.69

New force = 0.259 N

the magnitude of the electrostatic force F' that now acts on sphere 2 is 0.259 N

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