Let us suppose the magnitude of the original Coulomb force between the two charged spheres is FF. In this scenario, a third sphere touches the grey sphere and the red sphere multiple times, being grounded each touch. If the grey sphere is touched twice, and the red sphere is touched three times, what is the magnitude of the Coulomb force between the spheres now

F ’= 1/32 F

We see that the value of the force is the initial force over 32

Explanation:

In this problem the sphere that is touching the others is connected to ground, after each touch,

Let's analyze the charge of the gray sphere, when you touch it for the first time, the charge is divided between the two spheres each having Q / 2, when the sphere separates and touches ground, its charge passes zero. When I touch the gray dial again, its charge is reduced by half

½ (Q / 2) = ¼ Q

For the red dial repeat the same scheme

with the first touch the charge is reduced to Q / 2

with the second touch e reduce to ½ (Q / 2) = ¼ Q

with the third toce it is reduced to ½ (¼ Q) = ⅛ Q

Now let's analyze what happens to the electric force

if the force is F for when the charge of each sphere is Q

        F = k Q Q / r²

with the remaining charge strength is

        F ’= k (¼ Q) (⅛ Q) / r²

        F ’= 1/32 k Q Q / r²

        F ’= 1/32 F

We see that the value of the force is the initial force over 32

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