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 $AB=x$ (say)
$\therefore AC=\frac{x}{2},BC=\frac{x}{2}$
For the system to be in equilibrium
$F_{Qq}+F_{QQ}=0$
$\frac{1}{4\pi {\epsilon }_0}\frac{Qq}{(x/2{)}^2}+\frac{1}{4\pi {\epsilon }_0}\frac{QQ}{x^2}=0$ $\Rightarrow q=-\frac{Q}{4}$