Question

A proton and an electron, with same momenta, enter a magnetic field in a direction at right angles to the lines of force. If the radii of their circular paths arc $r_p$ and $r_e$ respectively then the value of $r_p:r_e$ will be

• A. $1:1$
• B. $1:2$
• C. $2:1$
• D. $4:1$

Answer 1

Answer: (A)

$1:1$

For a charged particle of mass $m$, charge $q$ entering into a magnetic field of induction $B$ in a direction at right angles to the lines of force, we can write
$\frac{m{v}^2}{r}=qBv$
$r=\frac{mv}{qB}$
For proton, $r_p=\frac{m_p{v}_p}{q_{p}B}$
For electron, $r_e=\frac{m_e{v}_e}{q_{e}B}$
Also, $m_p{v}_p=m_e{v}_e$ = constant.
Hence,
$\frac{r_p}{r_e}=\frac{q_e}{q_p}=\frac{1}{1}$ ......(since, $q_p=q_e$)