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Question #42349

Difficulty: 8/10 | 🟢 Free

The Question

A uniform conducting rod of length $L$ and resistance $r$ rotates with a constant angular velocity $\omega$ about one of its ends in a uniform magnetic field $B$ directed perpendicular to the plane of rotation. The free end of the rod slides on a fixed, frictionless, perfectly conducting circular ring. A stationary resistor of resistance $R$ is connected between the pivot and the ring. If the rod completes one full revolution, what is the work done by the magnetic force on the charge carriers, and the work done by the external mechanical agent to maintain the constant angular velocity, respectively?

Options

A.
$0$ and $\frac{\pi B^2 \omega L^4}{2(R+r)}$
B.
$\frac{\pi B^2 \omega L^4}{2(R+r)}$ and $\frac{\pi B^2 \omega L^4}{2(R+r)}$
C.
$-\frac{\pi B^2 \omega L^4}{2(R+r)}$ and $\frac{\pi B^2 \omega L^4}{2(R+r)}$
D.
$0$ and $\frac{\pi B^2 \omega L^4}{4(R+r)}$

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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

Conservative vs Non-conservative|Work-Energy Theorem for Rotation|Motional EMF in Rotating Rods

Why This Question Is Tricky

Common Mistakes

This question tests the fundamental misconception that the magnetic force does work to drive the induced current in a motional EMF setup.

Students frequently calculate the Joule heating energy and incorrectly attribute it to the work done by the magnetic field.

In reality, the Lorentz force on a moving charge is always perpendicular to its velocity, meaning the magnetic field does zero work.

The electrical energy dissipated in the resistors comes entirely from the mechanical work done by the external agent against the macroscopic magnetic drag (Laplace force), highlighting the non-conservative nature of the induced electric field and the proper application of the Work-Energy Theorem for rotating systems.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Work, Energy, and Power - Class 11 Part 1
Concept	Conservative vs Non-conservative
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free