question_answer

Two charge q and -3q are placed fixed on x-axis separated by distance d. Where should experience any force? 

A) \[\frac{d-\sqrt{2}d}{2}\]

B) \[\frac{d+\sqrt{3}d}{2}\]

C) \[\frac{d+3d}{2}\]

D) \[\frac{d-\sqrt{5}d}{2}\]

Correct Answer: B

Solution :

[b] Let a charge 2q be placed at P, at a distance I from A where charge q is placed, as shown in figure. The charge 2q will not experience any force, when force, when force of repulsion on it due to q is balanced by force of attraction on it due to  - 3q at B where \[AB=d\] or \[\frac{\left( 2q \right)\left( q \right)}{4\pi {{\varepsilon }_{0}}{{\ell }^{2}}}=\frac{\left( 2q \right)\left( -3q \right)}{4\pi {{\varepsilon }_{0}}{{\left( \ell +d \right)}^{2}}}\] \[=\,11\,\mu \,C.\] \[\therefore \ell =\frac{2d\pm \sqrt{4{{d}^{2}}+2{{d}^{2}}}}{4}=\frac{d}{2}\pm \frac{\sqrt{3}d}{2}\]