Question

An electron and a proton of equal linear momentum enter in the direction perpendicular to uniform magnetic field. If the radii of their circular paths be $r_e$ and $r_p$, respectively, then $\frac{r_r}{r_p}$ is equal to $m_e=$ mass of electron, $m_p=$ mass of proton.

• A. ${\left(\frac{m_p}{m_e}\right)}^{1/2}$
• B. $\frac{m_p}{m_e}$
• C. ${\left(\frac{m_e}{m_p}\right)}^{1/2}$
• D. $1$

Answer 1

The correct option is D $1$

Given, linear momentum of electron
= linear momentum of proton
or $M_c{V}_c=M_p{V}_p$
The radius of circular path is
$r=\frac{mv}{qB}$
For an electron the radius of circular path is
$r_p=\frac{m_e{v}_e}{qB}$
For a proton the radius of circular path is
$r_p=\frac{m_p{v}_p}{qB}$
Hence,
$\frac{r_e}{r_p}=1$