Question

Three equal charges $(q)$ are placed at corners of an equilateral triangle of side $a$. The force on any charge is

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

Answer 1

Answer: (B)

Let, find out force on charge at A.
$\therefore \vec{F}_{A B}=\frac{K(q)(q)}{a^{2}}=\frac{K q^{2}}{a^{2}}$
Similarly,
$\vec{ F }_{ AC }=\frac{ Kq ^{2}}{ a ^{2}}$
Now, Angle b/w $\vec{F}_{A B}\,\, \& \,\, \vec{F}_{A C}=60^{\circ}$
Using parallelogram of vector addition,
$\vec{F}_{r} 1 =\sqrt{\left(\vec{F}_{A B}\right)^{2}+\left(\vec{F}_{A C}\right)^{2}+2 \vec{F}_{A B} \vec{F}_{A C} \cos \theta}$
$=\sqrt{(3)\left(\frac{K q^{2}}{a^{2}}\right)^{2}}$
$=\frac{K q^{2}}{a^{2}} \sqrt{3} N$
All the three charges will experience the same force but in different dir.