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1. Electric Charges and Fields
medium
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 $\frac{Q}{q}=$ ______
A
$-2 \sqrt 2$
B
$-1$
C
$1$
D
$-$$\frac{1}{{\sqrt 2 }}$
(AIEEE-2009)
Solution
Let $F$ be the force between $Q$ and $Q .$ The force between $q$ and $Q$ should be attractive for net force on $Q$ to be zero. Let $F^{\prime}$ be the force between $Q$ and $q .$ For equilibrium
$\sqrt{2} F^{\prime}=-F$
$\sqrt{2} \times k \frac{Q q}{\ell^{2}}=-k \frac{Q^{2}}{(\sqrt{2} \ell)^{2}}$
$\Rightarrow \frac{Q}{q}=-2 \sqrt{2}$
Standard 12
Physics
