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It is clearly mentioned in the question that charge C is clamped .. By observation we see that charge C should be between A and B. Also note here that before introducing C ..A and B were repelling each othe..hence ..the charge C should attract A and B towards each other. ( finally A and B shud be at rest.) Hence C shud be negatively charged.( A and B are positively charged a and 2q) ..let charge on C be -Q. Now let C be at a distance x from A ..i.e. d-x distance from B. C is clampled ..not bothering C .. For A and B to be at rest ..the bet force on them should be zero. Net force on A = kq(-Q)/x^2 + kq(2q)/d^2 = 0 hence .. Q/x^2 = 2q/d^2 ......(1) Net force on B = k(2q)(-Q)/ (d-x)^2 + k(2q)(q)/d^2 = 0 hence .. Q/(d-x)^2 = q/d^2 ..(2) From (1) and (2) Q/ (d-x)^2 = Q/ 2x^2 2x^2 = (d-x)^2 root2.x = d-x x(1+root2) = d x = d / ( 1+root2) putting value of x in any of the above ..u'll get the value of Q.
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