Ions of unknown charge-to-mass ratio are to be selected for entry into a detector
PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Magnetism and Electromagnetism · Magnetism and Electromagnetism
Problem
Ions of unknown charge-to-mass ratio are to be selected for entry into a detector. The selection device consists of perpendicular electric and magnetic fields that occupy the same region of space. A uniform electric field of magnitude E points vertically upward (+z–direction). Particles enter the region traveling due east (+x–direction) with speed v. Only those particles that pass straight through without deflection are accepted.
(a) Determine the required direction (choose +y or −y) of a uniform magnetic field that will allow positively charged particles to pass undeflected. Justify your answer in terms of the net forces acting on the particles.
(b) Derive an expression for the magnitude B of the magnetic field that will ensure zero net force on a particle of charge +q traveling at speed v in the given electric field E. Express your answer in terms of E, v, and fundamental constants as needed.
(c) If the ions were negatively charged instead, explain how, if at all, the required magnetic field direction and magnitude would change for the selector to function properly.