= Gap field of a tapered electromagnet
{title2=$H_g=NI/[h+\mu_r^{-1}(Lr^2/R^2+2sr/R)]$}
A uniform-radius magnetic arc of <length> $L$ and <radius> $R$, two linear tapers of <length> $s$ to <radius> $r$, and an unfringed vacuum gap of <length> $h$ have the displayed gap field. Here $\mu_r=\mu/\mu_0$ and $B_g=\mu_0H_g$. Tapering concentrates flux, but at fixed winding current the gap-dominated limit is $H_g\simeq NI/h$ regardless of pole <area>. Saturation and leakage prevent unrestricted field enhancement.
Back to article page
