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Three charges 4q, Q and 2q are placed at positions 0, $l / 2$ and $l$ respectively along a straight line. If the resultant force on 2q is zero, then Q is equal to____

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$- 2 q$

$- q$

$- q / 2$

$4 q t$

answer is A.

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Detailed Solution

$Q = ? F_{Q} + F_{4 q} = 0$

$F Q = - F_{4 q}$

$\frac{1}{4 π ε_{0}} \frac{Q 2 q}{{(l / 2)}^{2}} = \frac{- 1}{4 π ε_{0}} \frac{2 q (4 q)}{l^{2}}$

$\frac{4 Q}{l^{2}} = \frac{- 4 q}{l^{2}}$

$Q = - q$

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