A narrow, straight beam of singly ionized calcium ions (each of charge ) travels in…
PHYSICS · Multi-part · AP · Physics C: Electricity and Magnetism · Magnetic Fields and Electromagnetism · Magnetic Fields and Electromagnetism
Problem
A narrow, straight beam of singly ionized calcium ions (each of charge +e) travels in vacuum past a magnetic-field sensor located a perpendicular distance d from the beam’s central axis. The sensor measures the magnetic field produced solely by the moving ions.
Initially the ion speed is v1 and the sensor records a magnetic field magnitude B1. Later, the sensor is repositioned so that its perpendicular distance from the beam becomes 1.5d, and at the same time the ion speed is increased to v2=1.8v1.
(a) Derive an expression for the magnetic field magnitude B measured at a perpendicular distance r from the beam in terms of fundamental constants, the ion speed v, and any other necessary quantities. Treat the beam as a line of point charges whose individual separations are large compared with atomic dimensions but small compared with r.
(b) Using your expression from part (a), determine the ratio B1B2 of the magnetic field magnitudes recorded in the two experimental setups.
(c) Explain qualitatively whether increasing the ion speed or increasing the sensor distance has the dominant effect on the change in the measured magnetic field, and justify your reasoning with reference to your result in part (b).