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Question

A rectangular loop of area \( 0.05 \, \text{m}^2 \) with 15 turns carries \( 2 \, \text{A} \) in a
field of \( 1 \, \text{T} \) at \( 90^\circ \) to the plane. What is the torque?

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Explanation

**Biot-Savart law** dB = μ₀/4π·I dl × r̂/r² underlies both straight wire and loop formulas. For square loop side a, area A = a², moment m = N I A, field pattern similar to dipole at large distances, with superposition for N turns. tau = N I A B sin θ , θ = 90° to plane means sin 0° = 1 with normal. tau = 15 × 2 × 0.05 × 1 × 1 = 1.5 N m . Using F = q v B sinθ, F = I l B sinθ, B = μ₀ I/(2π r), B = μ₀ N I/(2R) and τ

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