The $^{10}\mathrm{B}+n$ system has been studied by measuring charged particles from neutron-induced reactions in the 1 to 20 MeV energy range. Protons, deuterons, tritons, and $\ensuremath{\alpha}$ particles were measured at four angles using the pulsed white neutron spectrum at the Los Alamos Neutron Science Center Weapons Neutron Research facility. Differential cross sections for each species are reported. These new data are combined with literature data in an $R$-matrix analysis of the $^{11}\mathrm{B}$ compound system. A comparison is made to the molecular and cluster states candidates observed in these reactions.