An infinitely long conductor has cross-section in the form of a semicircular ring of radius R and carries total current I uniformly. Find the magnetic induction along its axis.
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An infinitely long conductor has cross-section in the form of a semicircular ring of radius R and carries total current I uniformly. Find the magnetic induction along its axis.

G1 Physics · Accepted Answer

Resolve the conductor into parallel line-current elements distributed uniformly along the semicircular arc. Integrating dB=μ₀dI/(2πR) with vector directions over 0 to π leaves the axial resultant B=μ₀I/(π²R). Hence B.