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Question #43276

Difficulty: 8/10 | 🟢 Free

The Question

An electron (charge $-e$ , effective mass $m^*$ ) is confined within a bulk semiconductor crystal and moves in a circular Bohr orbit corresponding to the principal quantum number $n=1$ . The semiconductor medium is isotropic and linear, with a relative magnetic permeability $\mu_r$ and relative permittivity $\epsilon_r$ . Assuming the Bohr model quantization of angular momentum applies, what is the magnitude of the effective macroscopic magnetic dipole moment of this system (including the contribution from the medium's induced magnetization)? Here, $h$ is Planck's constant.

Options

A.
$\frac{\mu_r e h}{4 \pi m^*}$
B.
$\frac{e h}{4 \pi m^*}$
C.
$\frac{\mu_r e h}{4 \pi \epsilon_r m^*}$
D.
$\frac{e h}{4 \pi \mu_r m^*}$

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

Magnetic Permeability and Susceptibility|Quantization of Angular Momentum|Magnetic Dipole Moment of Revolving Electron

Why This Question Is Tricky

Common Mistakes

This question tests the distinction between the bare Amperian magnetic moment and the effective macroscopic magnetic moment in a permeable medium.

Students commonly fall into two traps: (1) blindly applying the vacuum Bohr magneton formula while ignoring the medium's magnetization response (which scales the effective moment by $\mu_r$ due to bound currents), and (2) incorrectly assuming that the relative permittivity $\epsilon_r$ alters the magnetic moment.

While $\epsilon_r$ changes the orbital radius and velocity individually, their product (and thus the angular momentum) remains strictly fixed by Bohr's quantization condition, making the bare magnetic moment independent of the dielectric constant.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Magnetism and Matter - Class 12
Concept	Magnetic Permeability and Susceptibility
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free