Two positive equal charges are placed symmetrically about the origin on the $x$-axis and kept fixed as shown. Another positive charge $Q$ is placed at the origin. The charge $Q$ can be displaced by a very small distance $\delta$ to $P_1$ along the $x$-axis or to $P_2$ along the $y$-axis. Then,

• Correct answer
  A

  to the lowest order, the force on $Q$ at $P_2$ is proportional to $\delta$.
• B

  to the lowest order, the force on $Q$ at $P_1$ is proportional to $\delta^2$.
• C

  the charge $Q$ is in stable equilibrium with respect to small displacements along $y$-axis.
• Correct answer
  D

  the charge $Q$ is in stable equilibrium with respect to small displacements along the $x$-axis.

Hence, the correct answer is options: 'A', 'D'.