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Question #43434

Difficulty: 8/10 | 🟢 Free

The Question

An electron (mass $m$ , charge $-e$ ) moves in a stable circular orbit of radius $r$ with a constant speed $v$ , possessing an initial orbital angular momentum $\vec{L}_0$ . At time $t=0$ , a weak uniform external magnetic field $\vec{B}$ is applied such that the angle between $\vec{B}$ and $\vec{L}_0$ is $\theta$ ( $0 < \theta < \pi/2$ ). Assuming the magnitude of the orbital angular momentum $L = mvr$ remains strictly constant and the orbit acts as a rigid magnetic dipole, what is the magnitude of the change in the angular momentum vector, $|\Delta \vec{L}|$ , at time $t = \frac{\pi m}{eB}$ ?

Options

A.
$\sqrt{2} mvr \sin\theta$
B.
$\frac{\pi}{2} mvr \sin\theta$
C.
$2 mvr \sin\theta$
D.
$mvr \sin\theta$

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 Dipole Moment of Revolving Electron|Torque about non-fixed axes|Quantization of Angular Momentum

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to transition from static torque analysis to the dynamics of a precessing frame (Larmor precession).

A common trap is treating the magnetic dipole moment as a fixed scalar and calculating the change in angular momentum using a static torque approximation ( $|\Delta \vec{L}| \approx |\vec{\tau}|t = \frac{\pi}{2}mvr \sin\theta$ ), which ignores the continuous change in the direction of the torque.

Another lethal trap is confusing the Larmor precession frequency ( $\omega_p = eB/2m$ ) with the cyclotron frequency ( $\omega_c = eB/m$ ), which would lead to an incorrect precession angle of $\pi$ and a resulting change of $2mvr \sin\theta$ .

The correct approach requires recognizing the gyromagnetic ratio as the bridge between torque and precession angular velocity, and applying vector geometry to find the chord length of the precessing tip.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Magnetism and Matter - Class 12
Concept	Magnetic Dipole Moment of Revolving Electron
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free