Question

Three point charges $Q,q$ and $Q$ are placed along a straight line placed along $X$ axis at point $x=0,x=\frac{L}{2}$ and $x=L$ respectively. The entire system, of three charges will be in equilibrium, if

• A. $q=\frac{-Q}{4}$
• B. $q=\frac{Q}{4}$
• C. $q=\frac{-Q}{2}$
• D. $q=-Q$

Answer 1

The correct option is A $q=\frac{-Q}{4}$

$F_q=\frac{kq\times Q}{{\left(\frac{L}{2}\right)}^2}$

$F_Q=\frac{kQQ}{L^2}$

$F_q+F_Q=0$

$\frac{kqQ}{{\left(\frac{L}{2}\right)}^2}+\frac{k{Q}^2}{{\left(L\right)}^2}=0$

$\frac{4qQ}{L^2}=\frac{-Q^2}{L^2}$

$q=-\frac{Q}{4}$