Question

An electron and a proton of equal kinetic energy enter a uniform magnetic field normal to the lines of force. The radii of curvature of the circular paths be :

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

Answer 1

The correct option is D $\frac{r_e}{r_p}=\sqrt{\frac{m_e}{m_p}}$

Radius in magnetic field is given by,
$r=\frac{mv}{qB}=\frac{\sqrt{2mE}}{qB}$ where $E=\frac{p^2}{2m}$
$\therefore \frac{r_e}{r_p}=\frac{\frac{m_e^{1/2}}{q_e}}{\frac{m_p^{1/2}}{q_p}}=\sqrt{\frac{m_e}{m_p}}$