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Question #43385

Difficulty: 8/10 | 🟢 Free

The Question

A particle of mass $m$ and charge $q > 0$ is initially moving in a circular orbit of radius $r_0$ with speed $v_0$ in a uniform magnetic field $B_0$ . The magnetic field is directed perpendicular to the plane of the orbit. The magnetic field is slowly increased to $4B_0$ over a time interval $T$ (where $T$ is much larger than the time period of the orbit). Let $L_0 = m v_0 r_0$ and $K_0 = \frac{1}{2} m v_0^2$ be the initial angular momentum and kinetic energy of the particle. Which of the following represents the magnitude of the final angular momentum $L_f$ and final kinetic energy $K_f$ of the particle?

Options

A.
$L_f = L_0$ , $K_f = 4 K_0$
B.
$L_f = 4 L_0$ , $K_f = 16 K_0$
C.
$L_f = \frac{1}{4} L_0$ , $K_f = K_0$
D.
$L_f = 2 L_0$ , $K_f = 4 K_0$

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

Cyclotron Frequency Invariance|Angular Momentum conservation|Vector Cross-Products

Why This Question Is Tricky

Common Mistakes

This question tests the misconception that an induced electric field in a time-varying magnetic field must change the mechanical angular momentum of a charged particle.

Students often calculate the torque due to the induced electric field ( $\tau_E = q r E_\theta$ ) but completely ignore the torque from the magnetic field ( $\tau_B = -q r v_r B$ ) that arises because the orbit radius is shrinking ( $v_r \neq 0$ ).

In an adiabatic process, these two torques exactly cancel, conserving mechanical angular momentum, even though the kinetic energy increases due to the work done by the non-conservative electric field.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Moving Charges and Magnetism - Class 12
Concept	Cyclotron Frequency Invariance
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free