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.