Practice question
Question
A rectangular loop of area \( 0.03 \, \text{m}^2 \) with 20 turns carries \( 2 \, \text{A} \) in a
field of \( 0.7 \, \text{T} \) at \( 45^\circ \) 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 = 45° to plane means sin 45° with normal. tau = 20 × 2 × 0.03 × 0.7 × sin 45° = 0.84 × 0.707 = 0.5939 ≈ 0.59 N m . Using F = q v B sinθ, F = I l B sinθ, B =
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