question_answer

A charge q is placed at the centre of the line joining two equal charges Q. The system of the three charges will be in equilibrium if q is equal

A) \[-\frac{Q}{2}\]                                

B) \[-\frac{Q}{4}\]

C) \[+\frac{Q}{4}\]                               

D)        \[+\frac{Q}{2}\]

Correct Answer: B

Solution :

For equilibrium of Q \[\frac{Qq}{4\pi {{\varepsilon }_{0}}{{\left( \frac{l}{2} \right)}^{2}}}+\frac{{{Q}^{2}}}{4\pi {{\varepsilon }_{0}}{{l}^{2}}}=0\] \[\Rightarrow \]  \[4q+Q=0\] \[\Rightarrow \]  \[q=\frac{-Q}{4}\] Here we are asked to calculate equilibrium for system. In this system q is already in equilibrium. So, we are calculating equilibrium condition for Q.