Physics · Moving Charges and Magnetic Field

JEE Main 2025 — 7 April, Morning Shift — Question 57

Uniform magnetic fields of different strengths ( $B_{1}$ and $B_{2}$ ), both normal to the plane of the paper exist as shown in the figure. A charged particle of mass $m$ and charge $q$ , at the interface at an instant, moves into the region 2 with velocity $v$ and returns to the interface. It continues to move into region 1 and finally reaches the interface. What is the displacement of the particle during this movement along the interface?

Option A:
$\frac{m v}{q B_{1}}\left(1-\frac{B_{1}}{B_{2}}\right)$
Option B:
$\frac{m v}{q B_{1}}\left(1-\frac{B_{2}}{B_{1}}\right)$
Option C:
$\frac{m v}{q B_{1}}\left(1-\frac{B_{2}}{B_{1}}\right) \times 2$
Option D:
$\frac{m v}{q B_{1}}\left(1-\frac{B_{1}}{B_{2}}\right) \times 2$
Correct

Answer: D

Step-by-step solution

$R_{1}=\frac{m v}{q B_{1}}$

R_{2}=\frac{m v}{q B_{2}}

$|\Delta r|=\left|2 R_{2}-2 R_{1}\right|=\frac{2 m v}{q}\left[\frac{1}{B_{2}}-\frac{1}{B_{1}}\right]$

$\Rightarrow \quad \Delta r=\left|\frac{2 m v}{q B_{1}}\left[\frac{B_{1}}{B_{2}}-1\right]\right|=\left|\frac{2 m v}{q B_{1}}\left(1-\frac{B_{1}}{B_{2}}\right)\right|$

Answer key and solution verified before publishing.

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Exam: JEE Main 2025
Paper: 7 April, Morning Shift
Subject: Physics
Chapter: Moving Charges and Magnetic Field
Topic: Motion of Charged Particles in magnetic Fields