Two uniform magnetic fields B₁ and B₂, both perpendicular to the plane of the paper, occupy adjacent regions separated by a straight interface as shown in the original figure. A particle of mass m and charge q starts at the interface with speed v, enters region 2, returns to the interface, then moves through region 1 and reaches the interface again. Given B₂ > B₁, the displacement along the interface is:

Question

G1 Physics · Accepted Answer

A charged particle moving perpendicular to a magnetic field follows a circle of radius R = mv/(|q|B). In region 2, R₂ = mv/(|q|B₂), and the semicircular motion shifts the particle along the interface by diameter 2R₂. In region 1, R₁ = mv/(|q|B₁), and the corresponding semicircle shifts it by 2R₁ in the opposite sense. Hence the net displacement magnitude along the interface is Δx = 2R₁ - 2R₂ = (2mv/|q|)[1/B₁ - 1/B₂] = (2mv/|q|B₁)(1-B₁/B₂). This matches option D.