Question

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} $

Answer 1

Answer: (C)

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} $