Question

Work done to rotate a dipole from \( \theta_{1} = 0^\circ \) to \( \theta_{2} = 60^\circ \) is \( W \). The work required to rotate it to \( 180^\circ \) is:

• A. 2W
• B. 4W
• C. W
• D. 3W

Hint:

Maximum work is done when the dipole is rotated to a position exactly opposite to the field ($180^{\circ}$).

Answer 1

The Correct Option is B

Step 1: Concept
Work $W = pE(cos \theta_{1} - cos \theta_{2})$.
Step 2: Analysis
Case 1: $W = pE(1 - cos 60^{\circ}) = pE(1 - 0.5) = 0.5 pE$. Thus, $pE = 2W$. Case 2: $W_{2} = pE(1 - cos 180^{\circ}) = pE(1 - (-1)) = 2 pE$.
Step 3: Conclusion
$W_{2} = 2(2W) = 4W$.
Final Answer: (B)