Irodov Problem 3.384
Physics · electromagnetism · modern-physics · relativity
Problem
A non-relativistic electron originates at a point A lying on the axis of a straight solenoid and moves with velocity v at an angle a to the axis. The magnetic induction of the field is equal to B. Find the distance r from the axis to the point on the screen into which the electron strikes. The screen is oriented at right angles to the axis and is located at a distance 1 from the point A.Intuitive explanation
An electron entering a solenoid's uniform magnetic field undergoes helical motion—its velocity component parallel to the axis continues unchanged, while the perpendicular component causes circular motion in the plane perpendicular to . The key is to decompose the motion into these two independent parts: use the axial component to find the transit time to the screen, then use the circular motion's radius and angular displacement to determine where the electron hits.
Intuitive explanation
An electron entering a solenoid's uniform magnetic field undergoes helical motion—its velocity component parallel to the axis continues unchanged, while the perpendicular component causes circular motion in the plane perpendicular to . The key is to decompose the motion into these two independent parts: use the axial component to find the transit time to the screen, then use the circular motion's radius and angular displacement to determine where the electron hits.