Question

In a chamber, a uniform magnetic field of 6.5 G $(1G={10}^{-4}T)$ is maintained. An electron is shot into the field with a speed of $4.8\times {10}^{6}m{s}^{-1}$ normal to the field. Explain why the path of the electron is a circle. Determine the radius of the circular orbit. $(e=1.5\times {10}^{-19}C,m_e=9.1\times {10}^{-31}kg)$

Answer 1

Angle between electron and the magnetic field is ${90}^o$

$F=eVBsin\theta$, where e=charge on the electron.

F provide centripetal force to moving electron.

hence, it starts moving the circular path.

$F_c=m{v}^2/r$

in equilibrium, $F=F_c$

$\Rightarrow r=4.2cm$