Radius of the portion of the circular track inside magnetic field: r=mvqB=vqmB=2αdBαB=2d
Time period T=2πmqB=2πqmB=2παB
The particle spends half of T inside magnetic field.
Time spent inside magnetic field is T2=122παB=παB
Angle subtended by the path of charged particle in magnetic field at the center of circular path is π.