We present new longitudinal magnetic field and Stroemgren photometric measurements of the Bp star 84 UMa. From these data we determine a new rotational period P_rot_=1.38576+/-0.00080d, which is inconsistent with previously published values. The magnetic measurements indicate the presence of a weak, dominantly dipolar magnetic field in the photosphere of 84 UMa. We employ a new value of the rotational axis inclination in conjunction with the magnetic data in order to constrain the magnetic field geometry. We derive the following dipole oblique rotator parameters: i=59^+17^_-9_{deg}, {beta}=48^+17^_-29_{deg}, and B_d_=1620^+1270^_-30_G. A precise value of the radius (which we calculate in conjunction with the inclination using the Hipparcos parallax) allows us to locate 84 UMa on the radius-effective temperature plane. Using theoretical evolutionary tracks (Schaller et al., 1992, Cat. <J/A+AS/96/269>), we obtain values for the mass, age and surface gravity. These results place 84 UMa quite close to the ZAMS, a result inconsistent with the suggestion by Hubrig & Mathys (1994AN....315..343H) that the magnetic Ap stars may be near the end of their main sequence life.