A charge Q is placed at each of the opposite corners of a square. A charge q is placed at each of the other two corners. If the net electrical force on Q is zero, then Q/q equals

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$- 2 \sqrt{2}$

$- 1$

$1$

$- \frac{1}{\sqrt{2}}$

answer is A.

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Detailed Solution

It is given that

${\vec{F}}_{A} + {\vec{F}}_{B} + {\vec{F}}_{D} = 0$

Where ${\vec{F}}_{A}$ , ${\vec{F}}_{B}$ and ${\vec{F}}_{D}$ are the forces applied by charges placed at A, B and D on the charge placed at C.

$\Rightarrow {\vec{F}}_{B} + {\vec{F}}_{D} = - {\vec{F}}_{A}$

$| {\vec{F}}_{B} + {\vec{F}}_{D} | = \sqrt{2} \frac{k q Q}{a^{2}} & | {\vec{F}}_{A} | = \frac{k Q^{2}}{2 a^{2}}$

$∴ \sqrt{2} \frac{k q Q}{a^{2}} = - \frac{k Q^{2}}{2 a^{2}} \Rightarrow \frac{Q}{q} = - 2 \sqrt{2}$

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