Question

An electron and a proton enter a region of uniform magnetic field $B$ with uniform speed $v$ in a perpendicular direction.
What is the ratio of the radii of the circular paths of electrons to proton?

Answer 1

As $r=\frac{mv}{qB}\to r\infty m$
Ratio of radii of electron path and proton path.
$\frac{r_e}{r_p}=\frac{m_e}{m_p}$
As mass of proton $m_p\approx 1840\times$ amss of electron $\left(m_e\right)$
$\therefore \frac{m_e}{m_p}\approx \frac{1}{840}$ and $\frac{r_e}{r_p}=\frac{1}{1840}$