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Question #43874

Difficulty: 8/10 | 🟢 Free

The Question

Two infinitely long, parallel, frictionless conducting rails of zero resistance are separated by a distance $l$ . A straight conducting rod of mass $m$ and zero resistance is placed perpendicular to the rails. The rails are connected to an ideal DC voltage source of EMF $V_0$ , an ideal inductor of inductance $L$ , and a switch $S$ in series. A uniform, constant magnetic field of magnitude $B$ exists perpendicular to the plane of the rails. At $t=0$ , the switch $S$ is closed. Assuming the rod never leaves the rails, what is the maximum kinetic energy acquired by the rod during its subsequent motion?

Options

A.
$\frac{m V_0^2}{2 B^2 l^2}$
B.
$\frac{2 m V_0^2}{B^2 l^2}$
C.
$\frac{m V_0^2}{B^2 l^2}$
D.
$\frac{4 m V_0^2}{B^2 l^2}$

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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

Force on Current-Carrying Loop|L-C Circuit Analogy|Transient Current in RL Circuit

Why This Question Is Tricky

Common Mistakes

This question tests the electromechanical coupling in an RL circuit with a moving boundary, acting as an L-C circuit analogy.

Students commonly misapply the steady-state condition by setting $di/dt = 0$ to find the 'final' constant velocity $v = V_0 / (Bl)$ , and incorrectly calculate the kinetic energy as $m V_0^2 / (2 B^2 l^2)$ .

This ignores the inertial overshoot.

Because the system lacks resistance (no damping), the rod's velocity undergoes simple harmonic oscillation around the equilibrium velocity.

The true maximum velocity is twice the equilibrium velocity, making the maximum kinetic energy four times the steady-state assumption.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Electromagnetic Induction - Class 12
Concept	Force on Current-Carrying Loop
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free