Two charges $+q$ and $-q$ are placed at a distance $a$ in a uniform electric field. The dipole moment of the combination is $2qa(\cos \theta \hat{i} + \sin \theta \hat{j})$, where $\theta$ is the angle between the direction of the field and the line joining the two charges. Which of the following statement$(s)$ is/are correct?

  • A
    The torque exerted by the field on the dipole vanishes
  • B
    The net force on the dipole vanishes
  • C
    The torque is independent of the choice of coordinates
  • D
    The net force is independent of $a$

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