Question

Match Column-I with Column-II related to an electric dipole of dipole moment \( \vec{p} \) that is placed in a uniform electric field \( \vec{E} \): 

 

• A. \( a \rightarrow iii, b \rightarrow i, c \rightarrow ii \)
• B. \( a \rightarrow ii, b \rightarrow iii, c \rightarrow i \)
• C. \( a \rightarrow i, b \rightarrow ii, c \rightarrow iii \)
• D. \( a \rightarrow ii, b \rightarrow i, c \rightarrow iii \)

Hint:

The potential energy of a dipole in a uniform electric field is given by \( U = -pE \cos \theta \). The dipole's alignment with the field determines the energy: minimum at \( 0^\circ \), maximum negative at \( 180^\circ \), and zero at \( 90^\circ \).

Answer 1

The Correct Option is C

The potential energy of an electric dipole in a uniform electric field is given by: \[ U = - \vec{p} \cdot \vec{E} = -pE \cos \theta \] where: - \( \vec{p} \) is the dipole moment, - \( \vec{E} \) is the electric field, - \( \theta \) is the angle between \( \vec{p} \) and \( \vec{E} \), - \( p \) is the magnitude of the dipole moment. From this formula: 1. When the angle \( \theta = 0^\circ \) (i.e., the dipole is aligned with the electric field), the potential energy is minimum, and the work done by the electric field is: \[ W = pE \] 2. When the angle \( \theta = 180^\circ \) (i.e., the dipole is opposite to the electric field), the potential energy is maximum negative, and the work done by the electric field is: \[ W = -pE \] 3. When the angle \( \theta = 90^\circ \) (i.e., the dipole is perpendicular to the electric field), the potential energy is zero, and no work is done by the electric field. Thus, the correct matches are: \[ a \rightarrow i, b \rightarrow ii, c \rightarrow iii \]