In the x-y plane, the region y0 has a uniform magnetic field B₁k̂ and the region y

Question

In the x-y plane, the region y>0 has a uniform magnetic field B₁k̂ and the region y<0 has a uniform magnetic field B₂k̂. A positively charged particle is projected from the origin along the +y-axis with speed v₀=π m/s at t=0, as shown. Neglect gravity. Let T be the time when it crosses the x-axis from below for the first time. If B₂=4B₁, find its average speed along the x-axis during time T, in m/s.

G1 Physics · Accepted Answer

The particle moves at constant speed v₀=π m/s, tracing semicircles of radii r₁=mv/(qB₁) and r₂=r₁/4. Over the interval up to the first x-axis crossing from below, compute total x-displacement from the semicircle diameters and divide by total time (sum of half-cyclotron times). The result is 2 m/s.