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Question #43747

Difficulty: 8/10 | 🟢 Free

The Question

A continuous laser beam propagates along the $z$ -axis through a dilute, neutral gas of constant electric susceptibility $\chi$ . The time-averaged intensity of the beam varies radially as $I(r) = I_0 e^{-r^2/w^2}$ , where $r$ is the radial distance from the beam axis, $I_0$ is the peak intensity, and $w$ is the beam waist parameter. Although photons are electrically neutral, their oscillating electric fields induce a time-varying polarization in the gas molecules, resulting in a net time-averaged macroscopic volume force density $\vec{f}$ exerted on the gas. Assuming the gas is sufficiently dilute such that the speed of light in the medium is approximately $c$ (the speed of light in vacuum), what is the magnitude of the maximum radial force density exerted on the gas?

Options

A.
$\frac{\chi I_0}{c w \sqrt{2e}}$
B.
0
C.
$\frac{\sqrt{2} \chi I_0}{c w \sqrt{e}}$
D.
$\frac{\chi I_0}{c w e}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Multi-Concept_Bridge

Master problems that require linking physics and math concepts to solve complex competitive questions.

Concepts Behind This Question

Photon Neutrality|Dielectric Polarization Logic|Superposition of Potentials

Why This Question Is Tricky

Common Mistakes

This question targets the 'Photon Neutrality' misconception.

Students often incorrectly assume that because photons are electrically neutral, a light beam cannot exert a transverse electrostatic force on a neutral gas, leading them to choose zero.

The trap forces students to recognize that the photon's oscillating electric field induces a time-varying dipole moment in the medium.

Furthermore, they must apply the ponderomotive force principle, realizing that the spatial gradient of the beam's intensity creates a gradient in the electric field amplitude, which exerts a net force on these induced dipoles.

A secondary trap involves missing the factor of 1/2 in the energy of an induced dipole compared to a permanent dipole, which tests the precise application of dielectric polarization logic.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Dual Nature of Radiation and Matter - Class 12
Concept	Photon Neutrality
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free