Verified Solution • 2025–26 Session moderate

QPages 230-234: Q56: HC Verma: Concepts of Physics - Volume 2 Magnetic Field Pages 230-234: Q56 Solution: A circular coil of radius 2.0 cm has 500 turns and carries a…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students frequently calculate τ as N·I·A and stop, forgetting to multiply by the magnetic field strength B and the sine of the angle (sin θ). Always apply the full expression τ = N I A B sinθ to avoid under‑ or over‑estimating the torque.

A circular coil of radius 2.0 cm has 500 turns and carries a current of 1.0 A. Its axis makes an angle of 30� with the uniform magnetic field of magnitude 0.40 T that exists in the space. Find the torque acting on the coil.

Step-by-Step Verified Solution

**Answer:**

\tau = 0.628 \text{ N m}

. **Step-by-Step Explanation:**

N = 500

,

A = \pi (0.02)^2 = 1.26 \times 10^{-3} \text{ m}^2

,

i = 1 \text{ A}

,

B = 0.4 \text{ T}

,

\theta = 30^\circ

.

\tau = N i A B \sin\theta = 500 \times 1 \times 1.26 \times 10^{-3} \times 0.4 \times 0.5 = 0.126 \text{ N m}

.

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