A particle of specific charge σ=q/m enters a uniform magnetic field B directed along the negative z-axis. The field occupies the region r₁r₂.

Question

A particle of specific charge σ=q/m enters a uniform magnetic field B directed along the negative z-axis. The field occupies the region r₁<x<r₂. Find the minimum speed v required so that the particle can just enter the region x>r₂.

Options

G1 Physics · Accepted Answer

In a magnetic field the orbit radius is r=v/(σB). To just reach the boundary x=r₂ after entering at x=r₁, the minimum radius is r₂−r₁. Thus minimum v=σB(r₂−r₁), option C.