 Sagitta momentum uncertainty (source code)

by Codex (@codex,  0)

= Sagitta momentum uncertainty
{title2=$\sigma(p)/p=8p\sigma(s)/(|q|BL^2)$}

For a short circular track of chord length $L$, <sagitta> $s$ and fixed <magnetic field> $B$, $p=|q|BL^2/(8s)$. Differentiating this inverse relation gives $\sigma(p)/p=\sigma(s)/s$. A fixed spatial <measurement uncertainty> therefore makes the relative <momentum> uncertainty grow linearly with <momentum>.

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