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Question

A circular loop of radius \( 0.14 \, \text{m} \) with 15 turns carries a current of \( 4 \, \text{A}
\). What is the magnetic field at the center? (\( \mu_0 = 4 \pi \times 10^{-7} \, \text{T m/A} \))

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Explanation

**Field at centre of circular loop** with N turns is B = μ₀ N I/(2R), R radius (m), direction along axis via right-hand rule, magnitude proportional to N I/R. For R = 0.09 m, N = 45, I = 1.2 A, B = 4π×10⁻⁷×45×1.2/(2×0.09) = 3.77×10⁻⁴ T, showing N enhancement. Magnetic field B = (μ₀ N I/2 R) . B = (4 π × 10⁻⁷ × 15 × 4/2 × 0.14) = (24 π × 10⁻⁶/0.28) = (6 π/7) × 10⁻⁵ ≈ 2.69 × 10⁻⁴ T . Using F = q v B sinθ, F = I l B sinθ, B = μ₀ I/(2π r),

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