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An infinitely long straight conductor carries a current $I$ and has a cross-section shaped like a semicircular annulus of radius $R$. What is the magnitude of the magnetic field on its axis?
- $\mu_0 I/(2\sqrt{2}\,R)$
- $\mu_0 I/(2\pi R)$
- $\mu_0 I/(4\pi R)$
- $\mu_0 I/(\pi R)$
Correct answer: $\mu_0 I/(2\sqrt{2}\,R)$
Solution
The magnetic field on the axis of a current distribution with semicircular annular cross-section is obtained by integrating contributions from all current elements. By symmetry, only the axial component survives, and the integration yields $B=\mu_0 I/(2\sqrt{2}\,R)$.
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