Two charges $+q$ and $-q$ are placed at a distance $a$ in a uniform electric fleld. The dipole moment of the combination is $2 q a(\cos \theta i+\sin \theta)$. 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/ase correct?

• A

  The torque exerted by the field on the dipole vanishes
• Correct answer
  B

  The net force on the dipole vanishes
• Correct answer
  C

  The torque is independent of the choice of coordinates
• Correct answer
  D

  The net force is independent of a

Solution

The situation can be diagrammatically as, The dipole moment, $$ \mathbf{P}=2 q a(\cos \theta \hat{\mathbf{i}}+\sin \theta \hat{\mathbf{j}}) $$ The net force on the dipole is always zero while net torque on the dipole is not zero.

Hence, the correct answer is options: 'B', 'C', 'D'.