Question 865: Electrostats & Capacitance

Question

Three equal charges '$$\mathrm{q}_1$$', '$$^{\prime} \mathrm{q}_2$$' and '$$\mathrm{q}_3$$' are placed on the three corners of a square of side 'a'. If the force between $$\mathrm{q}_1$$ and $$\mathrm{q}_2$$ is '$$\mathrm{F}_{12}$$' and that between $$\mathrm{q}_1$$ and $$\mathrm{q}_3$$ is '$$\mathrm{F}_{13}$$', then the ratio of magnitudes $$\left(\frac{F_{12}}{F_{13}}\right)$$ is

Accepted Answer

Three equal charges are kept at the corners A, B, C of a square $$\mathrm{ABCD}$$.
$$	herefore$$ The force between $$\mathrm{q}_1$$ and $$\mathrm{q}_2$$ is $$\mathrm{F}_{12}$$
$$	ext { and } \mathrm{F}_{12}=\frac{1}{4 \pi \varepsilon_0} \frac{\mathrm{q} 	imes \mathrm{q}}{\mathrm{a}^2}=\frac{1}{4 \pi \varepsilon_0} \frac{\mathrm{q}^2}{\mathrm{a}^2}$$
and the force between $$\mathrm{q}_1$$ and $$\mathrm{q}_3$$ at $$\mathrm{A}$$ and $$\mathrm{C}$$ is
$$\begin{aligned}
& \mathrm{F}_{13}=\frac{1}{4 \pi \varepsilon_0} \frac{\mathrm{q}^2}{2 \mathrm{a}^2} \
& 	herefore \frac{\mathrm{F}_{12}}{\mathrm{~F}_{13}}=\frac{\mathrm{q}^2}{\mathrm{a}^2} 	imes \frac{2 \mathrm{a}^2}{\mathrm{q}^2}=2 	ext { (in magnitude) }
\end{aligned}$$

Answer

$$\frac{1}{2}$$

Answer

$$\sqrt{2}$$

Answer

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

Answer

$$2$$

Electrostats & Capacitance

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