Question

An electric dipole of dipole moment ' \(p\) ' is aligned parallel to a uniform electric field ' E '. The energy required to rotate the dipole by \(90^\circ\) is \( \begin{bmatrix} \sin 0^\circ = 0, & \sin 90^\circ = 1 \\ \cos 0^\circ = 1, & \cos 90^\circ = 0 \end{bmatrix} \)

• A. \(pE\)
• B. \(pE^2\)
• C. \(p^2E\)
• D. infinity

Hint:

Work done = change in potential energy of dipole.

Answer 1

The Correct Option is A

Concept:
Potential energy of a dipole in uniform electric field: \[ U = -pE \cos \theta \] Step 1: Initial position. Dipole is parallel to field: \[ \theta = 0^\circ \] \[ U_i = -pE \cos 0^\circ = -pE \]
Step 2: Final position. Dipole rotated by \(90^\circ\): \[ \theta = 90^\circ \] \[ U_f = -pE \cos 90^\circ = 0 \]
Step 3: Energy required. \[ \Delta U = U_f - U_i = 0 - (-pE) = pE \]
Step 4: Conclusion. Energy required = \(pE\)