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Question

A long straight wire carries a current of \( 25 \, \text{A} \). What is the magnetic field at a
distance of \( 0.25 \, \text{m} \) from it? (\( \mu_0 = 4 \pi \times 10^{-7} \, \text{T m/A} \))

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Explanation

**Biot-Savart law** dB = μ₀/4π·I dl × r̂/r² underlies both straight wire and loop formulas. For square loop side a, area A = a², moment m = N I A, field pattern similar to dipole at large distances, with superposition for N turns. Magnetic field B = (μ₀ I/2 π r) . B = (4 π × 10⁻⁷ × 25/2 π × 0.25) = (100 × 10⁻⁷/0.5) = 2 × 10⁻⁵ T . Using F = q v B sinθ, F = I l B sinθ, B = μ₀ I/(2π r), B = μ₀ N I/(2R) and τ = N I A B sinθ, result

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