question_answer

Three charges each of magnitude q are placed at the corners of an equilateral triangle, the electrostatic force on the charge placed at the center is (each side of triangle is L) [DPMT 2002]

A)            Zero                                         

B)            \[\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{{{q}^{2}}}{{{L}^{2}}}\]

C)            \[\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{3{{q}^{2}}}{{{L}^{2}}}\]    

D)            \[\frac{1}{12\pi {{\varepsilon }_{0}}}\frac{{{q}^{2}}}{{{L}^{2}}}\]

Correct Answer: A

Solution :

   In the following figure since \[|\overrightarrow{{{F}_{A}}}|\,=\,|\overrightarrow{{{F}_{B}}}|\,=\,|\overrightarrow{{{F}_{C}}}|\] and they are equally inclined with each other, so their resultant will be zero.