A particle of mass m and charge +q enters a region of magnetic field with a velocity v, as shown in Fig. 1.93.
a. Find the angle subtended by the circular arc described by it in the magnetic field.
b. How long does the particle stay inside the magnetic field?
c. If the particle enters at E, what is the intercept EF?

Explanation

(a) The particle circulates under the influence of magnetic field. As the magnetic field is uniform , the charge comes out symmetrically. The angle subtended at the centre is `(180-2 theta)`.
(b) The length of the arc traced by the particle, `l=R(pi-2theta)`
Time spent in the field, `t=l/v=(R(pi-2 theta))/v` and `R=(mv)/(Bq)`
which gives `t=m/(Bq)(pi-2 theta)`
As time period: `T=(2pim)/(Bq)`, hence `t=T/(2pi)(pi-2 theta)`

we can generalize this result, If `phi` is the angle subtended by the arc traced by the charged particle is the magnetic field, the time spent is `t=T(phi/(2pi))`
(c) Intercept `EF=2R cos theta`.