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Question #43671

Difficulty: 8/10 | 🟢 Free

The Question

A light beam consists of a linearly polarized component of intensity $I_0$ and an unpolarized component of intensity $I_0$ . The beam passes through an ideal analyzer rotating at a constant angular velocity $\omega$ . The emergent light illuminates a special photovoltaic cell. The cell generates an open-circuit EMF $E(t) = \alpha I(t)$ and has an internal resistance $r(t) = \beta I(t)$ , where $I(t)$ is the instantaneous intensity of the incident light, and $\alpha, \beta$ are positive constants. The cell is connected across a fixed coil of radius $a$ , having $N$ turns, self-inductance $L$ , and zero ohmic resistance. A small metallic ring of radius $b$ ( $b \ll a$ ) and resistance $R_0$ is placed concentrically and coplanar with the coil. Assuming the system has been operating for a long time, what is the time-averaged power dissipated due to eddy currents in the small metallic ring?

Options

A.
0
B.
$\frac{\mu_0^2 N^2 \pi^2 b^4 \alpha^2 \omega^2}{8 a^2 \beta^2 R_0}$
C.
$\frac{\mu_0^2 N^2 \pi^2 b^4 \alpha^2 \omega^2}{4 a^2 \beta^2 R_0}$
D.
$\frac{\mu_0^2 N^2 \pi^2 b^4 \alpha^2 \omega^2 L^2}{8 a^2 \beta^2 R_0 (L^2 \omega^2 + \beta^2 I_0^2)}$

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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

Photon Polarization and Selection|Internal Resistance Variation|Eddy Currents Dissipation|Calculus

Why This Question Is Tricky

Common Mistakes

This question tests a student's ability to couple quantum optical intensity variations with macroscopic circuit differential equations.

The primary trap lies in assuming that a time-varying light intensity must necessarily produce a time-varying current, leading students to calculate the current by treating the internal resistance as a constant average value.

By failing to set up the exact differential equation $E(t) - L(di/dt) = i(t)r(t)$ , they miss that the proportional variation of both the EMF and the internal resistance perfectly cancels out, resulting in a strictly constant steady-state current.

Consequently, the magnetic flux is static, and the eddy current dissipation is zero.

The distractor options represent the exact power dissipation if the internal resistance were incorrectly assumed to be constant.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Atoms - Class 12
Concept	Photon Polarization and Selection
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free