Question

An electric dipole placed in a non-uniform electric field experience:
A. Both a torque and a net force
B. Only a force but no torque
C. Only a torque but no net force
D. No torque and no net force

Answer 1

Hint: In a uniform electric field a dipole experiences torque but in a non-uniform electric field the electric field strength varies throughout so it would have an influence of an external force too.

Complete step by step answer:
Two equal and opposite charges separated by a small distance forms a dipole. Electric dipole moment measures the strength of a dipole p. It’s a vector quantity whose magnitude is either charge multiplied by the distance between the two charges and its direction is from negative to positive charge.
$p=q\times 2a$
When an electric dipole is placed in a uniform electric field it experiences a torque when the vector direction is not parallel to the electric field direction. It is given by:
$\overrightarrow{\tau }=\overrightarrow{p}\times \overrightarrow{E}$
This torque is perpendicular to both p and E and its direction is given by right hand screw rule.
Now, for a non-uniform electric field there will be a torque on the dipole but also a net force. Once the dipole comes parallel to the electric field vector a force will act on the dipole in the direction of increasing field.
Hence, the correct answer is A. Both torque and a net force

Additional Information:
Non uniform electric field is the one in which the electric field vectors are more closely spaced near the source charge and they get far apart as the distance from the source charge increases. Maximum torque acts on a dipole when the angle between P and E is maximum i.e. $\theta ={{90}^{{}^\circ }}$and its minimum when $\theta ={{0}^{{}^\circ }}$ in a uniform electric field.

Note: Option C. would be correct in case of a uniform electric field as the net force becomes zero since the force on opposite poles act in opposite direction and get cancelled out and only torque acts on the body as the forces are small distance apart. B. and D. are obviously incorrect since both force and torque are present.