Question

An electron and a proton of equal momentum enter a uniform magnetic field normal to the lines of force. If the radii of circular paths be $r_e$ and $r_p$, respectively, then

• A. $\left(\frac{r_e}{r_p}\right)=\left(\frac{1}{1}\right)$
• B. $\left(\frac{r_e}{r_p}\right)=\left(\frac{m_p}{m_e}\right)$
• C. $\left(\frac{r_e}{r_p}\right)=\sqrt{\frac{m_p}{m_e}}$
• D. $\left(\frac{r_e}{r_p}\right)=\sqrt{\frac{m_e}{m_p}}$

Answer 1

Answer: (A)

$\left(\frac{r_e}{r_p}\right)=\left(\frac{1}{1}\right)$

Radius of the circular orbit $r=\frac{mv}{qB}=\frac{p}{qB}$
Since $p$ is same for both electron and proton as given, $\frac{r_e}{r_p}=1$