Three equal charges $q_1, q_2$ and $q_3$ are placed on the three corners of a square of side $a$. If the…
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
$\frac{1}{\sqrt{2}}$
$\frac{1}{2}$
2
$\sqrt{2}$
Solution
Suppose the side of square is $a$. Then the diagonal is equal to $\sqrt{2} a$
$\begin{aligned} & \therefore F_{12}=\frac{1}{4 \pi \varepsilon_0} \frac{q_1 q_2}{a^2} \\ & \text { and } F_{13}=\frac{1}{4 \pi \varepsilon_0} \frac{q_1 q_3}{(\sqrt{2} a)^2}\end{aligned}$
We know, $q_1=q_2=q_3=q$
So, $\frac{F_{12}}{F_{13}}=\frac{2 q_2}{q_3}=2$