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Question #43381

Difficulty: 8/10 | 🟢 Free

The Question

An infinitely long straight wire carries a steady current $I$ in the positive $z$ -direction. The wire is kept parallel to the $z$ -axis and is undergoing constant acceleration $a$ along the positive $x$ -axis. At time $t=0$ , the wire passes through the origin ( $x=0, y=0$ ) with an instantaneous velocity $v_0 \hat{i}$ . At this exact instant ( $t=0$ ), a point charge $+q$ of mass $m$ is located at $(d, 0, 0)$ and is moving with velocity $\vec{v}_p = u \hat{i} + u \hat{j}$ . Assuming $v_0 \ll c$ such that the quasi-static approximation is valid (ignoring radiation effects), what is the instantaneous electromagnetic force vector on the particle at $t=0$ ?

Options

A.
$\frac{\mu_0 q I u}{2\pi d} \hat{k}$
B.
$\frac{\mu_0 q I (u - v_0)}{2\pi d} \hat{k}$
C.
$\frac{\mu_0 q I (u + v_0)}{2\pi d} \hat{k}$
D.
$-\frac{\mu_0 q I v_0}{2\pi d} \hat{k}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Intuition_Breaker

Train your brain to resist "obvious" answers that are designed to deceive your intuition.

Concepts Behind This Question

Lorentz Force Vector Direction|Magnetic Flux Scalar Sign|Derived Units via Fundamental Constants

Why This Question Is Tricky

Common Mistakes

This question tests the student's understanding of the Lorentz force in the context of a non-inertial, moving current source.

The primary trap is calculating only the magnetic force $\vec{F}_m = q(\vec{v} \times \vec{B})$ using the instantaneous Biot-Savart field, which leads directly to Option A.

Students often fail to recognize that a moving magnetic field source generates an induced electric field (via Faraday's Law, $\nabla \times \vec{E} = -\partial \vec{B}/\partial t$ ) in the lab frame.

By applying the low-velocity field transformation $\vec{E} = -\vec{v}_{source} \times \vec{B}$ , the problem reveals that the total electromagnetic force depends on the relative velocity between the charge and the source.

This is a profound relativistic concept that manifests even at non-relativistic speeds, forcing students to look beyond simple static formulas.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Moving Charges and Magnetism - Class 12
Concept	Lorentz Force Vector Direction
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free