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(C) Let the side length of the square be $a$. The charges are $q_1 = q_2 = q_3 = q$.According to Coulomb's Law,the force between two charges $q_i$ and

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$\frac{1}{2}$

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(C) Let the side length of the square be $a$. The charges are $q_1 = q_2 = q_3 = q$.According to Coulomb's Law,the force between two charges $q_i$ and $q_j$ separated by a distance $r$ is $F = \frac{k q_i q_j}{r^2}$.The distance between $q_1$ and $q_2$ is $r_{12} = a$. Thus,$F_{12} = \frac{k q^2}{a^2}$.The distance between $q_1$ and $q_3$ is the diagonal of the square,$r_{13} = a\sqrt{2}$. Thus,$F_{13} = \frac{k q^2}{(a\sqrt{2})^2} = \frac{k q^2}{2a^2}$.The ratio of $F_{13}$ to $F_{12}$ is $\frac{F_{13}}{F_{12}} = \frac{k q^2 / 2a^2}{k q^2 / a^2} = \frac{1}{2}$.

Three equal charges are placed on the three corners of a square as shown below. If the magnitude of force between $q_1$ and $q_2$ is $F_{12}$ and that between $q_1$ and $q_3$ is $F_{13}$,then the ratio of $F_{13}$ to $F_{12}$ is

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