Question

An electron emitted by a heated cathode and accelerated through a potential difference of 2.0 kV, enters a region with uniform magnetic field of 0.15 T. Determine the trajectory of the electron if the field (a) is transverse to its initial velocity, (b)
makes an angle of ${30}^{\circ }$ with the initial velocity.

Answer 1

(a)Kinectic energy of electron = eV

also, $eV=\frac{1}{2}m{v}^2$

$\Rightarrow v=\sqrt{2eV/m}-\left(1\right)$

also, $BeV=m{v}^2/r$

$\Rightarrow r=mV/Be$

using equation, $\left(1\right),r=1mm$

(b)$\theta ={30}^o$

$v_1=vsin\theta$

$r_1=mv\sin \theta /Be=0.5mm$