Question

When a dipole placed parallel to electric field is rotating through \(π^c\), the work done is W. The work done in rotating the dipole through \((\frac{π}{3})^c\) is
(\(cos0^{\circ} = 1\), \(cos60^{\circ} = \frac{1}{2}\), \(cos180^{\circ} = -1\))

• A. \(\frac{W}{4}\)
• B. \(\frac{W}{2}\)
• C. \(W\)
• D. \(2W\)

Hint:

Use W = pE(cos theta1 - cos theta2) with the dipole starting parallel to the field.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
The work done in rotating a dipole from angle \(\theta_1\) to \(\theta_2\) against the field is \(W = pE(\cos\theta_1 - \cos\theta_2)\).

Step 2: Key Formula or Approach:
The dipole starts parallel to the field, so \(\theta_1 = 0\) and \(\cos\theta_1 = 1\).

Step 3: Detailed Explanation:
Rotation through \(\pi\): \(W = pE(\cos 0^{\circ} - \cos 180^{\circ}) = pE(1 + 1) = 2pE\).
Rotation through \(\frac\pi3\): \(W' = pE(\cos 0^{\circ} - \cos 60^{\circ}) = pE\left(1 - \frac12\right) = \frac{pE}{2}\).
\[ \frac{W'}{W} = \frac{pE/2}{2pE} = \frac14 \]
So \(W' = \frac W4\).

Final Answer:
The work done is \(\frac{W}{4}\), option (A). \[ \boxed{\frac{W}{4}} \]