question_answer

Two charges \[+\text{ }q\]and \[-\text{ }q\]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

Correct Answer: B

Solution :

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