Question

Three charges $4\mu \text{C}$ each are kept at the vertices of an equilateral triangle of side $9\text{cm}$. The magnitude of force on one of the charges is

• A. $\frac{16\sqrt{3}}{9}\text{N}$
• B. $\frac{160}{9}\sqrt{3}\text{N}$
• C. $\frac{80}{9}\sqrt{3}\text{N}$
• D. $\frac{40}{9}\sqrt{3}\text{N}$

Answer 1

The correct option is B $\frac{160}{9}\sqrt{3}\text{N}$


$q=4\mu \text{C}=4\times {10}^{-6}\text{C};r=9\text{cm}$

The force on one of the charges , $F_{13}=F_{23}=F$

$F=\frac{1}{4\pi E_0}\frac{qq}{r^2}$

$\Rightarrow F=9\times {10}^9\times \frac{16\times {10}^{-12}}{(9\times {10}^{-2}{)}^2}=\frac{160}{9}\text{N}$

The resultant force , $F_R=\sqrt{F^2+F^2+2F^2\cos {60}^{\circ }}$

$\Rightarrow F_R=F\sqrt{2[1+\frac{1}{2}]}$

$\Rightarrow F_R=F\sqrt{3}=\frac{160}{9}\sqrt{3}\text{N}$.