Two charges Q and -3Q are placed fixed on x-axis separated by a distance 'd' Where should a third charge 2Q be placed such that it will not experience any force?

Explanation

Let charges Q and -3Q be placed at point A and B separated by a distance d. The third charge 2Q should be placed at point p on extension of line BA never the smaller charge of Q at distance x from it. As net force on 2Q charge is zero.
` therefore " " oversetto (F_(F)) =oversetto (F_(A)) +oversetto (F_(B)) =0 or oversetto (F_(A)) = oversetto (F_(B)) `
` rArr " "(1)/(4 pi in _0) .(Q(2Q))/(x^(2)) =(1)/(4 piin _0) ((-3Q)(2Q))/((x+d) ^(2))`
` rArr " " (1)/(x^(2)) =(3)/((x+d)^(2)) rArr x=(d)/((sqrt(3-1)) ) `