= Uniformly magnetized ring with a narrow gap
{title2=$H_g=lM/(l+a),\quad H_r=-aM/(l+a)$}
A rod of magnetic path length $l$ and tangential <magnetization> $M$ closed by a gap of width $a$ has constant flux in the one-dimensional <magnetic circuit> approximation. Equal cross sections and negligible leakage give $H_g=H_r+M$, while absence of free current gives $lH_r+aH_g=0$. Their solution is the displayed pair. Gap fringing or an unspecified cross-section change requires a more detailed field model.
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