Question

An electric dipole of dipole moment \(\vec{P}\) is placed in the uniform electric field \(\vec{E}\). Then which of the following statements are correct?
Statement I: The torque on the dipole is \(\vec{P} \times \vec{E}\)
Statement II: The potential energy of the dipole is \(-\vec{P} \cdot \vec{E}\)
Statement III: The net force on the dipole is non zero

• A. I, II and III
• B. I and II only
• C. II and III only
• D. I and III only

Hint:

If the electric field were non-uniform, then both a net torque and a net force would act on the dipole. Always check if the field is described as "uniform" or "non-uniform" in the problem statement.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question asks to evaluate three fundamental properties of an electric dipole when it is situated within a uniform external electric field.
Step 3: Detailed Explanation:
Statement I: The torque (\( \vec{\tau} \)) on a dipole in an external field is given by the cross product of the dipole moment and the field.
\( \vec{\tau} = \vec{P} \times \vec{E} \). Magnitude \( \tau = PE \sin\theta \).
This statement is correct.
Statement II: The electrostatic potential energy (\( U \)) of a dipole is the work done in bringing it from infinity (or a reference orientation of \( 90^{\circ} \)).
\( U = -PE \cos\theta = -\vec{P} \cdot \vec{E} \).
This statement is correct.
Statement III: In a uniform electric field, the force on the positive charge (\( +qE \)) and the force on the negative charge (\( -qE \)) are equal in magnitude and opposite in direction.
Net force \( \vec{F}_{net} = +q\vec{E} + (-q\vec{E}) = 0 \).
Therefore, the net force is zero.
Statement III says the net force is "non zero", so it is incorrect.
Step 4: Final Answer:
Only Statements I and II are correct. Hence, option (2) is the right answer.