Question

Consider $3$ identical charges of charge q placed at the vertices of an equilateral triangle, as shown in the figure. What is the force on one of the charges due to the others?

• A. $\frac{1}{4\pi {ϵ}_0}\frac{q^2}{l^2}$
• B. $\frac{\sqrt{2}}{4\pi {ϵ}_0}\frac{q^2}{l^2}$
• C. $\frac{\sqrt{3}}{4\pi {ϵ}_0}\frac{q^2}{l^2}$
• D. $\frac{2\sqrt{3}}{4\pi {ϵ}_0}\frac{q^2}{l^2}$

Answer 1

Answer: (C)

$\frac{\sqrt{3}}{4\pi {ϵ}_0}\frac{q^2}{l^2}$

Force between any two charges,

$F=\frac{k{q}^2}{l^2}$

Taking components, we get,

$F_{net}=2Fcos{30}^o=\frac{\sqrt{3}}{4\pi {ϵ}_0}\frac{q^2}{l^2}$