Question

An electron and a proton moving with the same speed enter the same magnetic field region at right angles to the direction of the field. For which of the two particles will the radius of circular path be smaller.

Answer 1

Fore on a charged particle in a magnetic field,

$F=qVB\sin \theta$

When $\theta =\frac{\pi }{2},F=qVB$ and for electron

$=qVB=\frac{m_e{V}^2}{r_e}$ (i)

For proton;

$qVB=\frac{m_p{V}^2}{r_p}$ (ii)

From equation i and ii;

$\frac{m_e}{m_p}=\frac{r_e}{r_p}$

$\because m_e<m_p$

$⟹r_e<r_p$ thus radius of electron is smaller.