Question

A narrow beam of protons and deuterons, each having the same momentum, enters a region of uniform magnetic field directed perpendicular to their direction of momentum. The ratio of the radii of the circular paths described by them is

• A. 1 : 2
• B. 1 : 1
• C. 2 : 1
• D. 1 : 3

Answer 1

Answer: (B)

Charge on deutron $\left(q_{d}\right)=$ charge on proton $\left(q_{p}\right)$
$q _{ d }= q _{ p }$
Radius of circular path $(r)=\frac{ P }{ Bq }\left(\therefore qvB =\frac{ mv ^{2}}{ r }\right)$
$r \propto \frac{1}{ q }[$ for constant momentum $( P )]$
So, $\frac{ r _{ p }}{ r _{ d }}=\frac{ q _{ d }}{ q _{ p }}=\frac{ q _{ p }}{ q _{ p }}=1$
Hence, $r_{p} ; r_{d}=1: 1$