Before You Begin

Question #43495

Difficulty: 8/10 | 🟢 Free

The Question

A U-shaped conducting frame of negligible resistance and width $L$ is rigidly fixed to a horizontal platform. The platform is pulled by an external mechanism, moving with a constant horizontal acceleration $a_0$ in the forward direction. A uniform vertical magnetic field $B$ is present throughout the region. A conducting rod of mass $m$ and resistance $R$ is placed across the rails of the U-frame and is free to slide without friction. The closed end of the U-frame is at the trailing edge (i.e., the open end faces the direction of acceleration). After a sufficient time, the rod reaches a steady state relative to the platform. In this steady state, what is the net mechanical power delivered by the macroscopic magnetic forces to the entire system (U-frame + rod) in the ground frame at time $t$ ?

Options

A.
$-\frac{m^2 a_0^2 R}{B^2 L^2}$
B.
$0$
C.
$\frac{m^2 a_0^2 R}{B^2 L^2}$
D.
$m a_0^2 t - \frac{m^2 a_0^2 R}{B^2 L^2}$

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

Pseudo Force Directionality|Force on Current-Carrying Loop|Frame of Reference

Why This Question Is Tricky

Common Mistakes

Students often memorize that 'magnetic forces do no work' and incorrectly choose 0, failing to distinguish between the microscopic Lorentz force on individual moving charges (which does no work) and the macroscopic magnetic force $I\vec{L}\times\vec{B}$ on a conductor (which can do mechanical work).

Furthermore, students who do calculate mechanical work often focus only on the sliding rod, forgetting that the magnetic field also exerts a force on the closed end of the accelerating U-frame.

By transforming to the ground frame, this problem forces students to reconcile the mechanical power balance, demonstrating that the net mechanical work done by macroscopic magnetic forces on the entire circuit exactly accounts for the electrical energy dissipated as Joule heating.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Laws of Motion - Class 11 Part 1
Concept	Pseudo Force Directionality
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free