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Question

A circular loop of radius \( 0.2 \, \text{m} \) with 10 turns carries \( 1.5 \, \text{A} \). What is
the magnetic field at its center? (\( \mu_0 = 4 \pi \times 10^{-7} \, \text{T m/A} \))

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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. Magnetic field B = (μ₀ N I/2 R) . B = (4 π × 10⁻⁷ × 10 × 1.5/2 × 0.2) = (6 π × 10⁻⁶/0.4) = 1.5 π × 10⁻⁵ ≈ 4.71 × 10⁻⁵ T . Using F = q v B sinθ, F = I l B sinθ, B = μ₀ I/(2π r), B = μ₀

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