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Question #43045
The Question
A toroid of mean radius has turns of wire carrying a steady current . The wire is wound with a uniform pitch such that the current path completes exactly one full revolution around the toroid's axis of symmetry (the -axis). The toroid lies in the -plane with its geometric center at the origin. A small rigid square loop of side length () carrying a steady current is placed at the origin. The small loop lies in the -plane and is rigidly mounted to a massless axle aligned with the -axis. Which of the following represents the magnitude of the magnetic torque acting on the small loop about the -axis?
Options
- A.
- B.
0
- C.
- D.
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
Toroidal Solenoid Boundary Conditions|Torque on Current Loop|Rigid Body Constraints
Why This Question Is Tricky
Common Mistakes
This question tests the limits of the 'ideal solenoid/toroid' approximation.
Students commonly memorize that the magnetic field outside an ideal toroid is strictly zero, leading them to incorrectly choose 0 as the torque.
However, in a physical toroid, the helical winding of the wire introduces a pitch, meaning the current has a net azimuthal component to close the circuit.
By the superposition principle, this acts as a single circular current loop of radius R, creating a non-zero 'leakage' magnetic field at the center.
The trap exploits the blind application of idealized boundary conditions while ignoring the physical reality of the winding constraint.
Quick Facts About This Question
Question Information
| Subject | Physics |
| Chapter | Moving Charges and Magnetism - Class 12 |
| Concept | Toroidal Solenoid Boundary Conditions |
| Difficulty | 8 |
| Cognitive Load | 7 |
| Target Solve Time | 160 sec |
| Access | Free |