Suppose the spheres A and B in question 1.12 have identical sizes. A third sphere of the same size but uncharged is brought in contact with the first, then brought in contact with the second, and finally removed from both. What is the new force of repulsion between A and B?

Charge on each of the sphere A and B = q = 6.5 x 10^–7 C

When a similar but uncharged sphere C is placed in contact with sphere A, each sphere shares a charge q/2, equally.
Now, if the sphere C is placed in contact with sphere 8, the charge is equally redistributed, so that
Charge on sphere B or C =

1 half left parenthesis straight q plus straight q divided by 2 right parenthesis space equals space 3 straight q divided by 4

Thus, the force of repulsion between A and B is

straight F space equals space fraction numerator 1 over denominator 4 πε subscript 0 end fraction. fraction numerator begin display style fraction numerator 3 straight q over denominator 4 end fraction end style. straight q divided by 2 over denominator left parenthesis straight r divided by 2 right parenthesis squared end fraction space space space space equals space 3 over 8. space fraction numerator 1 over denominator 4 πε subscript 0 end fraction. straight q squared over straight r squared space space space space space equals space 3 over 8 cross times 1.5 space cross times space 10 to the power of negative 2 end exponent straight N space space space space equals space 0.5625 space cross times space 10 to the power of negative 2 end exponent straight N space space space space equals 5.7 space cross times space 10 to the power of negative 3 end exponent straight N.

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