Practice question
Question
A rectangular loop of area \( 0.04 \, \text{m}^2 \) with 18 turns carries \( 2.8 \, \text{A} \) in a
field of \( 0.9 \, \text{T} \) at \( 60^\circ \) to the plane. What is the torque?
Explanation
**Magnetic field due to long straight wire** at distance r is B = μ₀ I/(2π r), μ₀ = 4π×10⁻⁷ T·m/A, direction circular around wire given by right-hand grip rule. For I = 18 A, r = 0.15 m, B = 2×10⁻⁷×18/0.15 = 2.4×10⁻⁵ T, illustrating 1/r dependence. tau = N I A B sin θ , where θ = 60° to plane means sin 30° with normal. tau = 18 × 2.8 × 0.04 × 0.9 × sin 60° = 1.8144 × 0.866 = 1.5712 ≈ 1.57 N m . Using F = q v B sinθ, F = I l B sinθ, B =
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