All Problems

Motion of Charged Particles in Electric and Magnetic Fields

Problem 3.384

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 \(\alpha\) 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 \(l\) from the point \(A\).

Reveal Answer
r=2ρsin(φ/2), where ρ=mveBsinα,φ=leBmvcosαr=2 \rho|\sin (\varphi / 2)|, \text { where } \rho=\frac{m v}{e B} \sin \alpha, \varphi=\frac{l e B}{m v \cos \alpha}