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. $\sqrt{3}\frac{K{q}^2}{a^2}$
• C. $\frac{K{q}^2}{\sqrt{3a^2}}$
• D. $3\sqrt{3}\frac{K{q}^2}{a^2}$

Answer 1

Answer: (B)

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