question_answer

A charge q is placed at the mid-point of the line joining two equal charges of Q. If the whole system is in equilibrium, then the value of q is

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

B)  \[+\frac{Q}{2}\]

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

D)  \[+\frac{Q}{4}\]

Correct Answer: C

Solution :

                 For system to be in equilibrium. The force between charges Q and q plus the force between charge Q and Q = 0. \[\Rightarrow \]               \[\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{Qq}{{{(l/2)}^{2}}}+\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{Q\theta }{{{l}^{2}}}=0\] or            \[\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{Q}{{{l}_{2}}}[4q+Q]=0\] or            \[4q+Q=0\]                 \[q=-\frac{Q}{4}\]