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A current-carrying wire of infinite length carries current i = 20/pi ampere. The wire is bent so that it has a semicircular arc of radius R = 1 m at its midpoint, with the two semi-infinite straight portions lying along the diameter (pointing away from the center) in the same plane. Find the magnitude of the magnetic field (in micro Tesla) at the center A of the semicircular arc.
- 2
- 4
- 6
- 8
Correct answer: 2
Solution
The two semi-infinite straight wire segments extend radially from the ends of the diameter. At center A, the position vector r from any element on these straight segments is along the direction of the current element dl, making dl cross r = 0. Hence the straight portions contribute zero field at A. Only the semicircle contributes: B_semi = mu0*i/(4R) = (4*pi*10⁻⁷ * 20/pi) / (4*1) = (80*10⁻⁷) / 4 = 2*10⁻⁶ T = 2 micro Tesla.
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