Three equal charges are placed on the three corners of a square. If the force between $q_{1}$ and $q_{2}$ is $F_{12}$ and that between $q_{1}$ and $q_{3}$ is $F_{13}$ , the ratio of magnitudes $\frac{F_{12}}{F_{13}}$ is

\frac{1}{2}

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2

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\frac{1}{\sqrt{2}}

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\sqrt{2}

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Solution

The correct option is B $2$
$F_{12} = \frac{1}{4 π ε_{0}} . \frac{q^{2}}{a^{2}}$ and $F_{13} = \frac{1}{4 π ε_{0}} . \frac{q^{2}}{(a \sqrt{2})^{2}} \Rightarrow \frac{F_{12}}{F_{13}} = 2$

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Three equal charges are placed on the three corners of a square. If the force between $q_{1}$ and $q_{2}$ is $F_{12}$ and that between $q_{1}$ and $q_{3}$ is $F_{13}$ , the ratio of magnitudes $\frac{F_{12}}{F_{13}}$ is

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