Before You Begin

Question #43420

Difficulty: 8/10 | 🟢 Free

The Question

Two infinitely long, straight, parallel wires are fixed at $x = a$ and $x = -a$ in a Cartesian coordinate system. Both wires carry a steady current $I$ in the positive $z$ -direction. A particle of mass $m$ and positive charge $q$ is projected from the origin $(0,0,0)$ with an initial velocity $\vec{v}_0 = v_0 \hat{j}$ . Neglecting gravity, what is the maximum $y$ -coordinate reached by the particle during its motion? (Define the dimensionless constant $K = \frac{2\pi m v_0}{q \mu_0 I}$ )

Options

A.
$a \sqrt{e^K - 1}$
B.
$a (e^K - 1)$
C.
$a \sqrt{e^{2K} - 1}$
D.
$a \ln(1 + K)$

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

Moving Charge in Non-Uniform B|Principle of Superposition|Centripetal Acceleration Vector

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to analyze non-uniform magnetic interactions using vector superposition and identify conserved quantities in non-separable differential equations.

The primary trap lies in the transition from standard planar circular motion to a complex trajectory.

Students often erroneously attempt to solve for the exact time-dependent path $y(t)$ or incorrectly assume the magnetic field does work, failing to recognize that integrating the Lorentz force over space (using the chain rule $v_y = dy/dt$ ) yields a conserved generalized momentum.

Additionally, a common mistake is missing the factor of 2 from the superposition of the two wires, leading to the distractor option C.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Moving Charges and Magnetism - Class 12
Concept	Moving Charge in Non-Uniform B
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free