A charged particle enters normally into a magnetic strip of width d

Question

A charged particle enters normally into a magnetic strip of width d<r, where r=mv/(|q|B). How long does it remain in the field before crossing the far boundary?

G1 Physics · Accepted Answer

The angular speed is ω=|q|B/m and the swept angle is φ=sin⁻¹(d/r). Therefore t=φ/ω=(m/|q|B)sin⁻¹(d/r).