Question

An electric dipole of moment \(\vec{p}\) is placed in a uniform electric field \(\vec{E}\). Then

• [(i)] the torque on the dipole is \(\vec{p}\times\vec{E}\).
• [(ii)] the potential energy of the system is \(\vec{p}\cdot\vec{E}\).
• [(iii)] the resultant force on the dipole is zero.

Choose the correct option.

• A. (i), (ii) and (iii) are correct
• B. (i) and (iii) are correct and (ii) is wrong
• C. Only (i) is correct
• D. (i) and (ii) are correct and (iii) is wrong

Hint:

Remember: \[ \vec{\tau}=\vec{p}\times\vec{E} \] \[ U=-\vec{p}\cdot\vec{E} \]

• Uniform electric field \(\Rightarrow\) zero net force
• Dipole experiences torque unless aligned with field

Answer 1

The Correct Option is B

Concept: An electric dipole placed in a uniform electric field experiences torque but no net force.

Step 1: Check statement (i). Torque on an electric dipole is given by: \[ \vec{\tau}=\vec{p}\times\vec{E} \] Hence statement (i) is correct.

Step 2: Check statement (ii). Potential energy of an electric dipole in an electric field is: \[ U=-\vec{p}\cdot\vec{E} \] But the statement says: \[ \vec{p}\cdot\vec{E} \] without the negative sign. Hence statement (ii) is incorrect.

Step 3: Check statement (iii). In a uniform electric field:

• Force on positive charge is \(+q\vec E\)
• Force on negative charge is \(-q\vec E\)

These forces are equal and opposite. Therefore: \[ F_{\text{net}}=0 \] Hence statement (iii) is correct. Therefore, the correct answer is: \[ \boxed{\text{(i) and (iii) are correct and (ii) is wrong}} \]