Question

Three charges $-$q, Q and $-$q are placed at equal distances on a straight line. If the total potential energy of the system of three charges is zero, then the ratio Q : q is

• A. $1:2$
• B. $2:1$
• C. $1:1$
• D. $1:4$

Answer 1

The correct option is D $1:4$

given $3$ charges $(-q,Q-q)$ are placed at equal distance on a straight line.
Total potential energy of the system will be, $[PE=(k\ast q^2)/2\ast d-(2\ast k\ast q\ast Q\left)/d\right]$
it is given that net potential energy is zero, therefore
$\left[\right(k\ast q^2)/2\ast d-(2\ast k\ast q\ast Q)/d=0]$

$⟹[q=4\ast Q]$