Question

Three charges each of magnitude q are placed at vertices of an equilateral triangle. A fourth charge -Q is placed at centroid of triangle so that system of 4 charges remains in equilibrium. Magnitude of charge Q is such that q = nQ, where n is (Answer upto two decimal places)

Answer 1

Q is in equilibrium due to symmetry.

For q,
$F\text{'}=2F\cos \left(\theta \right)(\theta ={30}^{\circ })\frac{KQq}{{\left(\frac{l}{\sqrt{3}}\right)}^2}=\frac{2K{q}^2}{l^2}\frac{\sqrt{3}}{2}\Rightarrow 3Q=\sqrt{3}q$