 Solution

The source labels $L$ as the full chord from $P_1$ to $P_3$, with $L/2$ on each side of its midpoint. The Right triangle between the Circle centre, chord midpoint and endpoint givesFor fixed geometry and field, the inverse transverse momentum isIf the uncertainty is dominated by the central point, ${\sigma }_s\simeq {\sigma }_x$. Linear propagation of uncertainty givesUsing $|q/e|=1$, $B=2\mathrm{T}$, $L=0.6\mathrm{m}$ and ${\sigma }_x=28.87\mu \mathrm{m}$,The inverse-momentum resolution is approximately momentum independent in this spatial-error-only model; the relative momentum resolution grows as $p_T\sigma (1/p_T)$. Endpoint errors and multiple scattering are excluded by the stated assumptions.