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Circuit and electromagnetism basics

In air, a current of 10 A flows in a long straight wire. Which is closest to the magnetic flux density at a point 10 cm from the wire? (μ0 = 4π×10⁻⁷ H/m; take the permeability of air as μ0.)

  1. AAbout 63 µT
  2. BAbout 126 µT
  3. C20 µT
Show answer and explanation

Answer: C. 20 µT

From Ampère's law, the flux density around a straight current is B = μ0I/(2πr): B = 4π×10⁻⁷ × 10/(2π × 0.1) = 2×10⁻⁵ T = 20 µT, comparable to the Earth's magnetic field (tens of µT). The flux density is inversely proportional to distance, halving to 10 µT at 20 cm.

  • A. About 63 µT uses μ0I/(2r), the formula for the center of a circular loop.
  • B. About 126 µT forgets to divide by 2π (μ0I/r).
  • C. Correct. 4π×10⁻⁷ × 10/(2π × 0.1) = 20 µT.
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