Question

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

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

Answer 1

The correct option is D $\frac{r_e}{r_p}=\frac{1}{1}$

$r=\frac{mv}{qB},wheremv\Rightarrow$ Momentum (P)
$\therefore r=\frac{P}{qB}$
$\text{Since both electron and proton have}\text{same charge and momentum}$
$\frac{r_e}{r_p}=\frac{1}{1}$