  We present our analysis of HD~35502 based on high- and medium-resolution
spectropolarimetric observations. Our results indicate that the magnetic
B5IVsnp star is the primary component of a spectroscopic triple system and that
it has an effective temperature of $18.4\pm0.6\,{\rm kK}$, a mass of
$5.7\pm0.6\,M_\odot$, and a polar radius of $3.0^{+1.1}_{-0.5}\,R_\odot$. The
two secondary components are found to be essentially identical A-type stars for
which we derive effective temperatures ($8.9\pm0.3\,{\rm kK}$), masses
($2.1\pm0.2\,M_\odot$), and radii ($2.1\pm0.4\,R_\odot$). We infer a
hierarchical orbital configuration for the system in which the secondary
components form a tight binary with an orbital period of $5.66866(6)\,{\rm d}$
that orbits the primary component with a period of over $40\,{\rm yrs}$.
Least-Squares Deconvolution (LSD) profiles reveal Zeeman signatures in Stokes
$V$ indicative of a longitudinal magnetic field produced by the B star ranging
from approximately $-4$ to $0\,{\rm kG}$ with a median uncertainty of
$0.4\,{\rm kG}$. These measurements, along with the line variability produced
by strong emission in H$\alpha$, are used to derive a rotational period of
$0.853807(3)\,{\rm d}$. We find that the measured $v\sin{i}=75\pm5\,{\rm
km\,s}^{-1}$ of the B star then implies an inclination angle of the star's
rotation axis to the line of sight of $24^{+6}_{-10}\degree$. Assuming the
Oblique Rotator Model, we derive the magnetic field strength of the B star's
dipolar component ($14^{+9}_{-3}\,{\rm kG}$) and its obliquity
($63\pm13\degree$). Furthermore, we demonstrate that the calculated Alfv\'{e}n
radius ($41^{+17}_{-6}\,R_\ast$) and Kepler radius
($2.1^{+0.4}_{-0.7}\,R_\ast$) place HD~35502's central B star well within the
regime of centrifugal magnetosphere-hosting stars.
