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Question #43169

Difficulty: 8/10 | 🟢 Free

The Question

A plane electromagnetic wave with electric field $\vec{E}_i = E_0 \cos(\omega t - kz) \hat{i}$ is incident normally on a thin, infinite resistive sheet located at $z=0$ . The sheet has a uniform surface conductivity $\sigma_s = \frac{4}{\mu_0 c}$ , such that the induced surface current density is $\vec{K} = \sigma_s \vec{E}_{sheet}$ . Here $\mu_0$ is the vacuum permeability, $\epsilon_0$ is the vacuum permittivity, and $c$ is the speed of light in vacuum. Determine the time-averaged radiation pressure $\langle P \rangle$ exerted on the sheet.

Options

A.
$\frac{2}{3} \epsilon_0 E_0^2$
B.
$\frac{2}{9} \epsilon_0 E_0^2$
C.
$\frac{1}{2} \epsilon_0 E_0^2$
D.
$\frac{4}{9} \epsilon_0 E_0^2$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Intuition_Breaker

Train your brain to resist "obvious" answers that are designed to deceive your intuition.

Concepts Behind This Question

Transverse Nature of EM Waves|Gauss Law Applicability|Symmetry and Virtual Work

Why This Question Is Tricky

Common Mistakes

This question targets a profound misconception regarding radiation pressure on partially absorbing/reflecting boundaries.

Students frequently assume that radiation pressure can be calculated merely by finding the absorbed intensity ( $I_{abs} = \frac{1}{2}\sigma_s E_t^2$ ) and dividing by $c$ , which incorrectly yields $\frac{2}{9}\epsilon_0 E_0^2$ .

They treat the dynamic wave interaction as a simple inelastic collision, ignoring the momentum carried away by the reflected and transmitted waves.

Furthermore, if attempting a microscopic force analysis, students often incorrectly use the total magnetic field on one side of the sheet rather than the average field $\vec{B}_{avg}$ acting on the surface current, or they mistakenly apply a static Gauss-like gradient $F=qE$ which averages to zero.

The correct approach requires either rigorous momentum conservation ( $p_{in} + p_{ref} - p_{trans}$ ) or evaluating the Lorentz force with the correct phase and average B-field.

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