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Question #43012

Difficulty: 8/10 | 🟢 Free

The Question

A particle of mass $m$ and charge $q > 0$ is initially moving in a circular orbit of radius $r_0$ in the $xy$ -plane, centered at the origin. A uniform magnetic field $\vec{B} = B_0 \hat{k}$ exists throughout the region. At $t=0$ , the magnetic field is abruptly decreased to $\vec{B} = \frac{B_0}{2} \hat{k}$ over a negligibly small time interval. What is the maximum distance of the particle from the origin during its subsequent motion?

Options

A.
$2 r_0$
B.
$\sqrt{2} r_0$
C.
$3 r_0$
D.
$1.5 r_0$

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|Conservative vs Non-conservative|Magnetic Flux Scalar Sign

Why This Question Is Tricky

Common Mistakes

This question tests the coupling of Faraday's law and the Lorentz force during an impulsive magnetic field change.

Students often fall into the trap of applying the adiabatic invariant ( $r^2 B = \text{constant}$ ) which yields $\sqrt{2} r_0$ , or assuming kinetic energy is conserved (ignoring the induced electric field's work) which yields $3 r_0$ .

Even if they calculate the new velocity and radius correctly, a secondary trap awaits: assuming the new circular orbit remains centered at the origin.

Because the change is abrupt, the particle's new trajectory is a shifted circle, requiring vector addition of the center's position and the new radius to find the true maximum distance.

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