Question

An electric dipole of dipole moment $\vec{P}$ is placed parallel to the uniform electric field of intensity $\vec{E}$. On rotating it through angle of 90° from this situation, the amount of work done is ______.

• A. $2PE$
• B. $\frac{PE}{2}$
• C. $PE$
• D. Zero

Hint:

Rotating from 0° to 180° (anti-parallel) requires the maximum work, which is $2PE$.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The potential energy of a dipole in an electric field is $U = -PE \cos\theta$. The work done in rotating the dipole is the change in its potential energy: $W = U_f - U_i$.
Step 2: Detailed Explanation:
Initial angle ($\theta_1$) = 0° (parallel to the field). Final angle ($\theta_2$) = 90°. $$W = -PE \cos(90^\circ) - (-PE \cos(0^\circ))$$ $$W = -PE(0) + PE(1)$$ $$W = PE$$
Step 3: Final Answer:
The work done is $PE$.