Question

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

• A. $0.9\text{N}$
• B. $1.8\text{N}$
• C. $2.7\text{N}$
• D. $3.6\text{N}$

Answer 1

The correct option is B $1.8\text{N}$

$F_A=$ force on $C$ due to charge placed at $A$
$=9\times {10}^9\times \frac{{10}^{-6}\times 2\times {10}^{-6}}{(10\times {10}^{-2}{)}^2}=1.8\text{N}$
$F_B=$ force on $C$ due to charge placed at $B$
$=9\times {10}^9\times \frac{{10}^{-6}\times 2\times {10}^{-6}}{(0.1{)}^2}=1.8\text{N}$
Net force on $C$
$F_{\text{net}}=\sqrt{(F_A{)}^2+(F_B{)}^2+2F_A{F}_B\times \cos {120}^{\circ }}=1.8\text{N}$