Question

Electric charges of $1 \,\mu C ,-1 \,\mu C$ and $2\, \mu C$ are placed in air at the corners $A, B$ and $C$, respectively, of an equilateral triangle $A B C$ having length of each side $10\, cm$. The resultant force on the charge at $C$ is

• A. 0.9 N
• B. 1.8 N
• C. 2.7 N
• D. 3.6 N

Answer 1

Answer: (B)

$F_{A}=$ Force on $C$ due to charge placed at $A$
$=9 \times 10^{9} \times \frac{10^{-6} \times 2 \times 10^{-6}}{\left(10 \times 10^{-2}\right)^{2}}=1.8 N$
$F_{B}=$ Force on $C$ due to charge placed at $B$
$=9 \times 10^{9} \times \frac{10^{-6} \times 2 \times 10^{-6}}{(0.1)^2}=1.8 N$

Net force on $C$,
$F_{ net }=\sqrt{\left(F_{A}\right)^{2}+\left(F_{B}\right)^{2}+2 F_{A} F_{B} \cos 120^{\circ}}=1.8 N$