Question

An electric dipole having dipole moment $P = q \times 2\ell$ is placed in a uniform electric field 'E'. The dipole moment is along the direction of the field. The force acting on it and its potential energy are respectively

• A. qE and minimum
• B. qE and maximum
• C. 2qE and minimum
• D. zero and minimum

Hint:

In a uniform electric field, the net forces always cancel out completely ($F = 0$). Furthermore, aligning a dipole *with* the field lines ($\theta = 0^\circ$) is its most natural, relaxed orientation, meaning its potential energy is minimized in this stable equilibrium position!

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
An electric dipole is placed in a uniform electric field such that its dipole moment vector ($\vec{P}$) is aligned parallel to the field lines. We need to determine the net electrostatic force acting on the dipole and its total potential energy.

Step 2: Detailed Explanation:
Let's analyze the force and energy profiles independently:

• Net Force Evaluation: An electric dipole consists of two equal and opposite point charges ($+q$ and $-q$) separated by a small distance. In a completely uniform electric field ($\vec{E}$), the positive charge experiences a force $\vec{F}_+ = +q\vec{E}$ in the direction of the field, and the negative charge experiences an equal and opposite force $\vec{F}_- = -q\vec{E}$ against the field direction. Summing these forces up: $$ \vec{F}_{\text{net}} = \vec{F}_+ + \vec{F}_- = q\vec{E} - q\vec{E} = \vec{0} $$ Therefore, the net force acting on any dipole inside a uniform field is always identically zero. ```

• Potential Energy Evaluation: The electrostatic potential energy (\(U\)) of an electric dipole inside an external electric field is given by the dot product formula: \[ U = -\vec{P} \cdot \vec{E} = -PE \cos\theta \] where \(\theta\) is the angle between the dipole moment vector and the electric field vector. The problem states that the dipole moment is aligned directly along the direction of the field, which means \(\theta = 0^\circ\). Substituting this angle: \[ U = -PE \cos(0^\circ) = -PE(1) = -PE \] Since \(-PE\) is the most negative possible value for this energy function, the potential energy of the system is at its absolute minimum value, representing a state of stable equilibrium. ```


Step 3: Final Answer:
The net force and potential energy are zero and minimum respectively, which corresponds to option (D).