Two charges, each equal to $-q$ are kept at $(-a, 0)$ and $(a, 0)$. A charge $q$ is placed at the origin. If $q$ is given a small displacement along y direction, the force acting on q is proportional to

• A

  $y$
• Correct answer
  B

  -y
• C

  $\frac{1}{y}$
• D

  $-\frac{1}{y}$

Solution

$\vec{F}=+q$ (Electric field due to the two negative charges $=\vec{E}$ ) $$ \vec{F}=+q\left[\frac{k(-2 q) \vec{y}}{a^3}\right] \Rightarrow \vec{F}=-\frac{2 k q^2 y}{a^3} \Rightarrow \vec{F} \propto-\vec{y} $$

Hence, the correct answer is option: 'B'.