First slide

Electrostatic force

Question

Three equal charges each having charge +q are placed at the corners of an equilateral triangle of side a. Then the Coulomb force experienced by one charge due to rest of the two is

Moderate

A

$\frac{1}{4 π \in_{0}} \frac{q^{2}}{a^{2}}$
B

$\frac{1}{4 π \in_{0}} \frac{2 q^{2}}{a^{2}}$
C

$\frac{1}{4 π \in_{0}} \frac{\sqrt{3} q^{2}}{a^{2}}$
D

$z e r o$

Solution

The force due to the two charges on the third charge be $F_{1}$ and $F_{2}$ , then
$F_{1} = F_{2} = \frac{1}{4 π \in_{0}} \frac{q^{2}}{a^{2}}$
They act along the sides of triangle and angle between the forces is $60^{\circ}$ .
So the resultant force on the third charge is
$\begin{array}{l} = \sqrt{F_{1}^{2} + F_{2}^{2} + 2 F_{1} F_{2} \cos 60^{\circ}} \\ = \sqrt{F^{2} + F^{2} + 2 F^{2} (\frac{1}{2})} \\ = \sqrt{3 F^{2}} = \sqrt{3} F \\ F_{R} = \frac{1}{4 π \in_{0}} \frac{\sqrt{3} q^{2}}{a^{2}} \end{array}$
Therefore, the correct answer is (C)

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