Question

The work done in rotating an electric dipole of dipole moment $p$ in a uniform electric field $E$ from $\theta = 0^\circ$ to $\theta = 180^\circ$ is:

• A. $pE$
• B. $2pE$
• C. Zero
• D. $-2pE$

Hint:

Electric Dipole Energy Relation: Potential Energy of Dipole: $U = -pE\cos\theta$ Minimum energy occurs at $\theta = 0^\circ$ (stable equilibrium). Maximum energy occurs at $\theta = 180^\circ$ (unstable equilibrium).

Answer 1

The Correct Option is B

Concept: An electric dipole consists of two equal and opposite charges separated by a small distance. The dipole moment is defined as: \[ p = q \times 2a \] where $q$ is the magnitude of each charge and $2a$ is the separation between them. When a dipole is placed in a uniform electric field, it experiences a torque that tends to align the dipole with the direction of the field. The potential energy of an electric dipole in a uniform electric field is given by: \[ U = -pE\cos\theta \] where $p$ = dipole moment
$E$ = electric field strength
$\theta$ = angle between dipole moment and electric field.

Step 1: Find the initial potential energy. At $\theta = 0^\circ$, \[ U_i = -pE\cos 0^\circ \] \[ U_i = -pE \]

Step 2: Find the final potential energy. At $\theta = 180^\circ$, \[ U_f = -pE\cos 180^\circ \] Since $\cos 180^\circ = -1$, \[ U_f = +pE \]

Step 3: Calculate work done. The work done in rotating the dipole equals the change in potential energy. \[ W = U_f - U_i \] \[ W = pE - (-pE) \] \[ W = 2pE \] Therefore, the work required to rotate the dipole from $0^\circ$ to $180^\circ$ is: \[ \boxed{2pE} \]