Question

Electrons in a beam are accelerated from rest through a potential difference `Delta V`. The beam enters an experimental chamber through a small hole. As shown in Fig. 1.35, the electron velocity vector lie within a narrow cone of half angle `phi` oriented along the beam axis. We wish to use a uniform magnetic field directed parallel to the axis to focus the beam, so that all of the electrons can pass through a small exit port on the opposite side of the chamber after they travel the length d of the chamber. What is the required magnitude of the magnitude field?

Answer 1

`d=n(v cosphi)T=(vcosphi)(2pimn)/(qB), where n=1,2,3,.....`
where `eDeltaV=1/2mv^2`
`v=sqrt((2DeltaVe)/m)`
Putting the value, we get `B=n/d (2pim)/q (sqrt((2DeltaVe)/m)) cosphi`
for min`B,n=1`