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 $ABC$ having length of each side $10cm$. 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 $A$
$=9\times 10^9\times \frac{10^{-6}\times 2\times 10^{-6}}{{\left(10\times 10^{-2}\right)}^2}=1.8N$
$F_B=$ Force on $C$ due to charge placed at $B$
$=9\times 10^9\times \frac{10^{-6}\times 2\times 10^{-6}}{(0.1{)}^2}=1.8N$

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