PHYSICS · Multi-part · CBSE · Physics · Moving Charges and Magnetism · Moving Charges and Magnetism
Problem
Inside a vacuum chamber, a positively charged particle travels at constant speed along a straight horizontal track of length L. A set of deflection plates gradually tilts the particle’s velocity vector upward while a uniform magnetic field remains directed vertically upward throughout the region. The arrangement is such that the angle between the particle’s velocity and the magnetic field increases uniformly from 0∘ at the entrance (x=0) to 90∘ at the exit (x=L). Assume the speed of the particle does not change.
(a) Express the angle θ(x) between the velocity and the magnetic field as a function of the particle’s horizontal position x along the track.
(b) Using the relationship from part (a), construct a qualitative graph of the magnitude of the magnetic force on the particle as a function of x for 0≤x≤L. Clearly indicate the behavior at the endpoints and any symmetry or monotonic features.
(c) Identify the region along the track where the magnetic force increases most rapidly with position, and explain your reasoning.
(d) Describe how the direction of the magnetic force evolves as the particle travels from x=0 to x=L, making explicit reference to a right-hand rule.