Magnetic Dipole Moment And Torque On A Loop
A rectangular coil of 50 turns and area 2×10−2 m2 carries a current of 1.5 A while placed in a field of 0.4 T with its plane parallel to the field; what torque acts on the coil?
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About This Question
- Subject
- physics
- Chapter
- magnetic effects of current and magnetism
- Topic
- magnetic dipole moment and torque on a loop
- Difficulty
- Hard
- Year
- 2025
Solution
Correct Answer:
0.6 N·m
As explained in NCERT Class 12, Chapter 4 (Moving Charges and Magnetism), a current loop of N turns, area A, carrying current I in a field B has a magnetic dipole moment m=NIA and experiences a torque τ=mBsinθ=NIABsinθ, where θ is the angle between the field and the coil's normal. When the coil's plane is parallel to the field, its normal is perpendicular to the field, so θ=90∘ and sinθ=1, giving maximum torque. Substituting N=50, I=1.5 A, A=2×10−2 m2, B=0.4 T: τ=(50)(1.5)(2×10−2)(0.4)=0.6 N·m. The value 0.3 N·m arises from halving the turns. The value 1.2 N·m doubles the area. The 'zero' choice wrongly assumes the plane parallel to the field gives no torque, confusing plane orientation with normal orientation. Plausibility check: units give A⋅m2⋅T=N\cdotpm, confirming a torque, and a sub-newton-metre value is typical for a small multi-turn coil. Note also that if the coil's plane were instead perpendicular to the field, the normal would be aligned with the field, θ would be zero, and the torque would vanish, which is the exact opposite of the maximum-torque situation described here, reinforcing that this configuration gives the largest possible twist.
This hard difficulty physics question is from the chapter magnetic effects of current and magnetism, covering the topic of magnetic dipole moment and torque on a loop. It appeared in the 2025 exam.
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