Three equal charges q_1, q_2 and q_3 are plac | vedclass

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(C) Let the side of the square be $a$. The distance between adjacent corners is $a$,and the distance between opposite corners (diagonal) is $\sqrt{2}a

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$2$

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(C) Let the side of the square be $a$. The distance between adjacent corners is $a$,and the distance between opposite corners (diagonal) is $\sqrt{2}a$.According to Coulomb's Law,the force between two charges is $F = \frac{1}{4 \pi \varepsilon_0} \frac{q_i q_j}{r^2}$.For charges $q_1$ and $q_2$ at adjacent corners,the distance is $r = a$. Thus,$F_{12} = \frac{1}{4 \pi \varepsilon_0} \frac{q_1 q_2}{a^2}$.For charges $q_1$ and $q_3$ at opposite corners,the distance is $r = \sqrt{2}a$. Thus,$F_{13} = \frac{1}{4 \pi \varepsilon_0} \frac{q_1 q_3}{(\sqrt{2}a)^2} = \frac{1}{4 \pi \varepsilon_0} \frac{q_1 q_3}{2a^2}$.Given $q_1 = q_2 = q_3 = q$,we have:$\frac{F_{12}}{F_{13}} = \frac{\frac{1}{4 \pi \varepsilon_0} \frac{q^2}{a^2}}{\frac{1}{4 \pi \varepsilon_0} \frac{q^2}{2a^2}} = \frac{1}{1/2} = 2$.

Three equal charges $q_1, q_2$ and $q_3$ are placed on the three corners of a square of side $a$. If the 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 magnitudes $\left(\frac{F_{12}}{F_{13}}\right)$ is

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