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.
$\Rightarrow$ $\frac{1}{4\pi {\epsilon }_0}\frac{Qq}{{(l/2)}^2}+\frac{1}{4\pi {\epsilon }_0}\frac{Q\theta }{l^2}=0$ or $\frac{1}{4\pi {\epsilon }_0}\frac{Q}{l_2}[4q+Q]=0$ or $4q+Q=0$ $q=-\frac{Q}{4}$