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

Step 1: Understanding the Concept:
An electric dipole placed in an external electric field has potential energy which depends on its orientation relative to the field.
Work must be done by an external agent to change this orientation.
Step 2: Key Formula or Approach:
Potential energy of dipole: \(U = -pE \cos \theta\).
Work done (energy required): \(W = \Delta U = U_f - U_i = pE (\cos \theta_i - \cos \theta_f)\).
Step 3: Detailed Explanation:
Initial state: Aligned parallel to the field, so \(\theta_i = 0^\circ\).
Final state: Rotated by \(90^\circ\), so \(\theta_f = 90^\circ\).
Substitute values into the work formula: \[ W = pE (\cos 0^\circ - \cos 90^\circ) \] Using the given trigonometric values: \[ W = pE (1 - 0) = pE \] Step 4: Final Answer:
The energy required is \(pE\).