Question

Electrons (mass m, charge –e) are accelerated from rest through a potential difference V
and are then deflected by a magnetic field B

that is perpendicular to their velocity. The radius of the resulting electron trajectory is:

Answer 1

The velocity of the electron can be computed as,

$$ \begin{aligned} \frac{1}{2} m v^{2} &=e V \\ v &=\sqrt{\frac{2 e V}{m}} \end{aligned} $$

When the electron enters the magnetic field,

$$ \begin{aligned} \frac{m v^{2}}{r} &=e v B \\ r &=\frac{m v}{e B} \\ &=\frac{1}{B} \sqrt{\frac{2 V m}{e}} \end{aligned} $$