A particle of mass m and charge +Q enters a magnetic-field half-plane normally with speed v. Its time in the field is T₁. Repeating with charge -Q gives time T₂. If T=2πm/(QB), find T₁/T₂ for the geometry shown.

Question

G1 Physics · Accepted Answer

Both charges have the same radius r=mv/(QB) but bend in opposite senses. From the chord geometry, the angles swept in the field are π+2θ for +Q and π-2θ for -Q. Time is proportional to swept angle, so T₁/T₂=(π+2θ)/(π-2θ). Hence A.