Question

Two electric dipoles, each of dipole moment ‘P’, are placed at points A (\(a,0\)) and B (\(-a,0\)) as shown in the figure. The work done in rotating both the dipoles through 90° in clockwise direction is (E = Electric field)

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

Hint:

For symmetric configurations, the net work done in rotating dipoles in an electric field can be zero due to cancellation of forces.

Answer 1

The Correct Option is B

The work done to rotate a dipole in an electric field is given by the equation: \[ W = -\vec{p} \cdot \vec{E} (\cos \theta_2 - \cos \theta_1) \] Where: - \( \vec{p} \) is the dipole moment, - \( \vec{E} \) is the electric field, - \( \theta_1 \) and \( \theta_2 \) are the initial and final angles of the dipole. For the given case, since the dipoles are arranged symmetrically and rotated through 90° in the clockwise direction, the net work done is zero. Thus, the correct answer is: \[ \boxed{\text{Zero}} \]