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QPages 230-234: Q54: HC Verma: Concepts of Physics - Volume 2 Magnetic Field Pages 230-234: Q54 Solution: A 50-turn circular coil of radius 2.0 cm carrying a current of…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often mix up the angle in the torque formula: τ = N I A B sin φ uses φ as the angle between the magnetic field and the coil’s normal, not the plane. If you treat the given angle as between field and plane, the expression becomes τ = N I A B cos θ; using the wrong trigonometric function leads to an incorrect angle (e.g., 60° instead of 30°). Always define the angle clearly and use sin for normal‑field and cos for field‑plane relationships.

A 50-turn circular coil of radius 2.0 cm carrying a current of 5.0 A is rotated in a magnetic field of strength 0.20 T. a) What is the maximum torque that acts on the coil? b) In a particular position of the coil, the torque acting on it is half of this maximum. What is the angle between the magnetic field and the plane of the coil?

Step-by-Step Verified Solution

**Answer:** (a)

\tau_{max} = 0.314 \text{ N m}

(b)

\theta = 30^\circ

. **Step-BY-Step Explanation:** (a)

\tau_{max} = N i A B = 50 \times 5 \times \pi (0.02)^2 \times 0.20 = 0.314 \text{ N m}

. (b)

\tau = \tau_{max} \cos\theta = \tau_{max}/2 \Rightarrow \cos\theta = 1/2 \Rightarrow \theta = 60^\circ

.

All Questions in this Chapter

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