Question

Three positive charge each of magnitude Q are placed at the corner of the equilateral tringle . The value of charges placed at the centroid of the triangle such that system must be in equilibrium is

• A. $\frac{+Q}{\sqrt{3}}$
• B. $\frac{-Q}{\sqrt{3}}$
• C. $\frac{-2Q}{\sqrt{3}}$
• D. $\frac{+2Q}{\sqrt{3}}$

Answer 1

The correct option is B $\frac{-Q}{\sqrt{3}}$

$\begin{array}{c}Letthelengthofthesideofthetrianglebel\\ LetADbetheperpendiculartothesideBC\\ \therefore AD=ACCu{30}^{\circ }=l\times \frac{\sqrt{3}}{2}\\ Let{}^{\prime }{o}^{\prime }becentroidfromA.\\ =\frac{2}{3}\times AD=\frac{2}{3}\times \frac{\sqrt{3}}{2}=\frac{1}{\sqrt{3}}\\ But,Ao=Bo=Co,\left(bysymmetry\right)\\ Thus,forthesystemtoreamininequilibrium,thechangeqshouldbe=\frac{-Q}{\sqrt{3}}\\ Hence,theoptionBisthecorrectanswer.\end{array}$