Question

A narrow beam of protons and deutrons, each having the same momentum, enters a region of uniform magnetic field directed perpendicular to their direction of momentum. What would be the ratio of the circular paths described by them?
OR
A proton and a deuteron having equal momenta enter in a region of uniform magnetic field at right angle to the direction of the field. Find the ratio of the radii of curvature of the path of the particle.

Answer 1

Charge on deutron $\left(q_d\right)=$ charge on proton $\left(q_p\right)$
$q_d=q_p$
Radius of circular path $\left(r\right)=\frac{P}{Bq}(\therefore qvB=\frac{m{v}^2}{r})$
$r\propto \frac{1}{q}$ [for constant momentum $\left(P\right)$]
So, $\frac{r_p}{r_d}=\frac{q_d}{q_p}=\frac{q_p}{q_p}=1$
Hence, $r_p;r_d=1:1$