Question

If a charge $q$ is placed at the centre of the line joining two equal charges $Q$ such that the system is in equilibrium then the value of $q$ is :

• A. $Q / 2$
• B. $-Q / 2$
• C. $Q / 4$
• D. $-Q / 4$

Answer 1

Answer: (D)

Let charge q is placed at mid point of line AB as shown below.

Also $A B=x$ (say)
$\therefore A C=\frac{x}{2}, B C=\frac{x}{2}$
For the system to be in equilibrium
$F_{ Qq }+F_{Q Q}=0$
$\frac{1}{4 \pi \varepsilon_{0}} \frac{Q q}{(x / 2)^{2}}+\frac{1}{4 \pi \varepsilon_{0}} \frac{Q Q}{x^{2}}=0$ $\Rightarrow q =-\frac{Q}{4}$