A mass spectrometer accelerates two types of singly charged ions into a region where…
PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Magnetism and Electromagnetism · Magnetism and Electromagnetism
Problem
A mass spectrometer accelerates two types of singly charged ions into a region where a uniform magnetic field of magnitude 0.080T points in the +y-direction. Both ions enter the field travelling along the +x-direction, so the velocity is perpendicular to the field. Ion 1 has speed 1.5×106m/s, while ion 2 has speed 2.0×106m/s. Ion 1 is positively charged and ion 2 is negatively charged, with each having charge magnitude equal to the elementary charge e.
(a) Derive an algebraic expression for the magnitude of the magnetic force on one of these ions in terms of the ion’s charge magnitude q, its speed v, and the magnetic field magnitude B.
(b) Use your result from part (a) to calculate the ratio of the magnetic force on ion 2 to that on ion 1.
(c) For ion 1, indicate whether the magnetic force points in the +z or −z direction and justify your answer using an appropriate right-hand or left-hand rule.