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Question #43097

Difficulty: 8/10 | 🟢 Free

The Question

A long ideal solenoid is completely filled with a paramagnetic fluid of uniform magnetic susceptibility $\chi$ . A steady current flows through the solenoid's windings, establishing a magnetic field. A particle of mass $m$ and charge $q$ is projected inside the fluid with a speed $v$ ( $v \ll c$ ) in a plane perpendicular to the solenoid's axis. The particle undergoes uniform circular motion of radius $R$ . Assuming the fluid does not exert any viscous drag on the particle, what is the magnitude of the magnetization vector $|\vec{M}|$ of the paramagnetic fluid? (Let $\mu_0$ be the permeability of free space)

Options

A.
$\frac{\chi m v}{\mu_0 (1 + \chi) q R}$
B.
$\frac{\chi m v}{\mu_0 q R}$
C.
$\frac{(1 + \chi) m v}{\mu_0 \chi q R}$
D.
$\frac{m v}{\mu_0 (1 + \chi) q R}$

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Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Variable_Constraint

Develop pure symbolic logic skills by mastering algebraic constraints without relying on numerical data.

Concepts Behind This Question

Magnitude Ratio Identity|Magnetic Permeability and Susceptibility|Superposition of Magnetic Fields

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to distinguish between the total magnetic field $\vec{B}$ (which dictates the Lorentz force on a moving charge) and the auxiliary field $\vec{H}$ (the source field).

A common trap is to incorrectly assume that the external field $\vec{B}_0 = \mu_0 \vec{H}$ is responsible for the circular motion, or to use the approximation $\vec{B} \approx \mu_0 \vec{H}$ when calculating magnetization via $\vec{M} = \chi \vec{H}$ , leading to the erroneous result $M = \chi B / \mu_0$ .

The student must correctly apply the superposition principle $\vec{B} = \mu_0(\vec{H} + \vec{M})$ to find the exact magnitude ratio identity between $\vec{M}$ and the dynamically experienced $\vec{B}$ .

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Electromagnetic Waves - Class 12
Concept	Magnitude Ratio Identity
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free