Chapter 25: Motion of Charged Particles

When a charged particle moves through a magnetic field, it experiences a force perpendicular to both its velocity and the field direction, described by the relationship F equals BQv when motion is perpendicular to field lines, where B represents magnetic flux density, Q is the particle charge, and v is velocity. This perpendicular force causes particles to follow circular paths, with the magnetic force providing centripetal acceleration. The radius of this circular orbit depends on particle mass and charge, increasing for faster or more massive particles and decreasing for stronger fields or higher charge values. These principles enable practical applications including particle accelerators and mass spectrometers, which exploit the mass-dependent orbital behavior to separate particles by their charge-to-mass ratios. Velocity selectors demonstrate how perpendicular electric and magnetic fields can be balanced to allow only particles moving at a specific speed to pass undeflected, with the selection velocity determined by the ratio of electric to magnetic field strength. The Hall effect describes a voltage generated perpendicular to both an applied magnetic field and current flow through a conductor, arising when moving charge carriers are deflected by the magnetic force, creating charge separation until an internal electric field balances the deflection. This Hall voltage relates directly to magnetic field strength, making Hall probes valuable instruments for field measurement, particularly when constructed from semiconductors that generate larger measurable voltages. The chapter concludes by illustrating how these combined field principles enabled groundbreaking discoveries, particularly J.J. Thomson's determination of the electron's charge-to-mass ratio through crossed field experiments and Robert Millikan's subsequent measurement of elementary charge through oil drop analysis, fundamentally establishing the electron as a discrete subatomic particle.