# Q 1.13: Suppose the spheres A and B in Exercise 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?

H Harsh Kankaria

When two spheres of same size are touched, on attaining equipotential state, the total charge of the system is equally distributed on both of them.

Therefore, (i) When uncharged third sphere,C, is touched with A, charge left on A = $0.5\times 6.5\times 10^{-7}C$

and charge attained by C = $0.5\times 6.5\times 10^{-7}C$

(ii) Now, Charge on B + Charge on C = $6.5\times 10^{-7}C$ + $0.5\times 6.5\times 10^{-7}C$ = $1.5\times 6.5\times 10^{-7}C$

When touched, Charge left on B =  $0.5\times1.5\times 6.5\times 10^{-7}C$

Therefore $q_{A}\rightarrow 0.5\times q_{A}\ and\ q_{B}\rightarrow 0.75\times q_{B}$

Therefore, $F' = 0.5\times0.75 \times F = 0.375 \times 1.5\times10^{-2} N = \boldsymbol{5.7\times10^{-3}\ N}$

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