Practice question
Question
A circular loop of radius \( 0.08 \, \text{m} \) with 60 turns carries a current of \( 0.75 \, \text{A}
\). What is the magnetic field at the center? (\( \mu_0 = 4 \pi \times 10^{-7} \, \text{T m/A} \))
Explanation
**Torque on current loop** in magnetic field B is τ = N I A × B, magnitude τ = N I A B sinθ, N turns, I current (A), A area (m²) = l×b for rectangular, θ angle between normal to plane and B. Maximum when plane parallel to B (θ=90°), zero when perpendicular (θ=0°), magnetic moment m = N I A direction along normal via right-hand rule. Magnetic field B = (μ₀ N I/2 R) . B = (4 π × 10⁻⁷ × 60 × 0.75/2 × 0.08) = (18 π × 10⁻⁶/0.16) = 1.125 π × 10⁻⁴ ≈ 3.53 × 10⁻⁴ T .
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