Practice question
Question
A circular loop of radius \( 0.13 \, \text{m} \) with 20 turns carries a current of \( 3.5 \, \text{A}
\). What is the magnetic field at the center? (\( \mu_0 = 4 \pi \times 10^{-7} \, \text{T m/A} \))
Explanation
**Field outside long solenoid** considered negligible because magnetic lines are concentrated inside and return path spreads over large area outside, making B_out ≈ 0. This justifies using solenoid for uniform field experiments, with n = 950 m⁻¹, I = 1.4 A giving B = 4π×10⁻⁷×950×1.4 = 1.67×10⁻³ T. Magnetic field B = (μ₀ N I/2 R) . B = (4 π × 10⁻⁷ × 20 × 3.5/2 × 0.13) = (28 π × 10⁻⁶/0.26) = 1.0769 π × 10⁻⁴ ≈ 3.38 × 10⁻⁴ T . Using F = q v B sinθ, F = I l B sinθ, B = μ₀ I/(2π r), B =
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