Question

Three equal charges each +Q, placed at the corners of on equilateral triangle of side a what will be the force on any charge $\left( k = \frac{1}{4\pi\varepsilon_{0}} \right)$

• A. $\frac{kQ^{2}}{a^{2}}$
• B. $\frac{2kQ^{2}}{a^{2}}$
• C. $\frac{\sqrt{2}kQ^{2}}{a^{2}}$
• D. $\frac{\sqrt{3}kQ^{2}}{a^{2}}$

Answer 1

Answer: (D)

$\frac{\sqrt{3}kQ^{2}}{a^{2}}$

Answer 2

Suppose net force is to be calculated on the charge which is kept at A. Two charges kept at B and C are applying force on that particular charge, with direction as shown in the figure.

Since $F_{b} = F_{c} = F = k\frac{Q^{2}}{a^{2}}$

So, $F_{net} = \sqrt{F_{B}^{2} + F_{C}^{2} + 2F_{B}F_{C}\cos 60}$

$F_{net} = \sqrt{3}F = \frac{\sqrt{3}kQ^{2}}{a^{2}}$