question_answer

Three charges\[{{Q}_{0}},-q\]and\[-q\]are placed at the vertices of an isosceles right angle triangle as in the figure. The net electrostatic potential energy is zero if\[{{Q}_{0}}\]is equal to

A)  \[\frac{q}{4}\]                 

B)         \[\frac{2q}{\sqrt{32}}\]

C)  \[\sqrt{2q}\]    

D)         \[+q\]

E)  \[\frac{q}{\sqrt{2}}\]

Correct Answer: B

Solution :

Here total electrostatic potential energy is zero ie,           \[\frac{-{{Q}_{0}}q}{l}-\frac{q{{Q}_{0}}}{l}+\frac{{{q}^{2}}}{\sqrt{2}l}=0\] On solving,          \[{{Q}_{0}}=\frac{q}{2\sqrt{2}}=\frac{2q}{\sqrt{32}}\]