Before You Begin

Question #43091

Difficulty: 8/10 | 🟢 Free

The Question

A uniform, perfectly absorbing semi-circular disc of mass $M$ and radius $R$ lies in the $xy$ -plane, occupying the region $x \ge 0$ . Its straight edge is hinged along the $y$ -axis, allowing it to rotate freely about the $y$ -axis. The disc has a total permanent electric dipole moment $\vec{p} = p_0 \hat{k}$ uniformly distributed over its surface.

A linearly polarized plane electromagnetic wave pulse travels in the $+z$ -direction, illuminating the entire semi-disc. The electric field of the pulse at $z=0$ is given by $\vec{E}(t) = E_0 \sin(\omega t) \hat{i}$ for $0 \le t \le \pi/\omega$ , and $\vec{E}(t) = 0$ otherwise.

Assuming the pulse duration is extremely short such that the disc does not rotate significantly during the pulse, what is the magnitude of the angular velocity acquired by the disc immediately after the pulse passes?

Options

A.
$\frac{4}{M R^2 \omega} \left| 2 p_0 E_0 - \frac{\pi R^3 \epsilon_0 E_0^2}{3} \right|$
B.
$\frac{4}{M R^2 \omega} \left( 2 p_0 E_0 + \frac{\pi R^3 \epsilon_0 E_0^2}{3} \right)$
C.
$\frac{8 p_0 E_0}{M R^2 \omega}$
D.
$\frac{4 \pi R \epsilon_0 E_0^2}{3 M \omega}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Variable_Constraint

Develop pure symbolic logic skills by mastering algebraic constraints without relying on numerical data.

Concepts Behind This Question

Transverse Nature of EM Waves|Angular Momentum conservation|Instantaneous Nature

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to synthesize classical rigid body dynamics with the microscopic and macroscopic interactions of electromagnetic waves.

The 'lethal trap' lies in treating radiation pressure as the sole mechanical effect of an EM wave, ignoring the direct instantaneous torque exerted by the transverse electric field on the material's permanent dipoles.

Furthermore, students often mistakenly assume that a linearly polarized wave cannot transfer angular momentum.

By forcing the integration of both the $\vec{p} \times \vec{E}$ torque and the asymmetric radiation pressure torque over the ultra-short pulse duration, the problem exposes the misconception that EM wave interactions are purely scalar pressure phenomena, demanding rigorous vector analysis of competing angular impulses.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Electromagnetic Waves - Class 12
Concept	Transverse Nature of EM Waves
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free