A Hall probe, consisting of a thin rectangular slab of current-carrying material, is calibrated by placing it in a known magnetic field of magnitude 0.10 T. When the field is oriented normal to the slab’s rectangular face, a Hall emf of 12 mV is measured across the slab’s width. The probe is then placed in a magnetic field of unknown magnitude $B$, and a Hall emf of 63 mV is measured. Determine $B$ assuming that the angle $\theta$ between the unknown field and the plane of the slab’s rectangular face is

1. $\theta = 90 ^\circ$, and
2. $\theta = 60 ^\circ$
.