A particle of charge 'q' and mass 'm' enters normally (at point P) in a region of magnetic field with speed v. It comes out normally from Q after time T as shown in figure. The magnetic field B is present only in the region of radius R and is uniform. Initial and final velocities are along radial direction and they are perpendicular to each other. For this to happen, which of the following expression(s) is/are correct :-

Question

G1 Physics · Accepted Answer

Inside the field, the path is a quarter circle of radius R because initial and final radial velocities are perpendicular. Thus qvB=mv²/R ⇒ B=mv/(qR). Quarter-circle time is (πR/2)/v=πR/(2v)=πm/(2qB). Hence A,B,C.