Step 1: Understanding the Concept:
An electric dipole consists of a pair of equal and opposite point charges ($+q$ and $-q$) separated by a small distance. When introduced into a uniform external electric field, the behavior of the dipole depends on the fact that the electric field magnitude and direction are perfectly identical at every point across space.
Step 2: Detailed Explanation:
Let us analyze each statement rigorously using mechanical and electrostatic formulas:
- Statement (i): The positive charge $+q$ experiences an electrical force $\vec{F}_+ = +q\vec{E}$, and the negative charge experiences an equal and opposite force $\vec{F}_- = -q\vec{E}$. These forces act at different positions, creating a couple that generates a twisting rotational effect. The torque ($\vec{\tau}$) acting on an electric dipole is expressed as the cross product of the dipole moment vector and the electric field vector:
\[ \vec{\tau} = \vec{p} \times \vec{E} \]
Thus, statement (i) is correct.
- Statement (ii): The electrostatic potential energy ($U$) stored within an electric dipole system inside an external field represents a scalar quantity derived via a dot product. The standard formula is:
\[ U = -\vec{p} \cdot \vec{E} \]
Statement (ii) omits the essential negative sign, claiming the energy is $+\vec{p} \cdot \vec{E}$. Thus, statement (ii) is wrong.
- Statement (iii): Calculate the net resultant translational force ($\vec{F}_{\text{net}}$) acting on the dipole system:
\[ \vec{F}_{\text{net}} = \vec{F}_+ + \vec{F}_- = (+q\vec{E}) + (-q\vec{E}) = 0 \]
Because the field is perfectly uniform, the opposing forces cancel out completely, meaning there is zero net translational movement. Thus, statement (iii) is correct.
Reviewing our conclusions, statements (i) and (iii) are correct, while statement (ii) is wrong, which corresponds precisely to option (B).
Step 3: Final Answer:
The correct option is (B): (i) and (iii) are correct and (ii) is wrong.