Question

A proton and a deutron both having the same kinetic energy, enter perpendicularly into a uniform magnetic field B. For motion of proton and deutron on circular path of radius $R_p$ and $R_d$ respectively, the correct statement is

• A. $R_d=\sqrt{2}{R}_p$
• B. $R_d=\frac{R_p}{\sqrt{2}}$
• C. $R_d=R_p$
• D. $R_d=2R_p$

Answer 1

The correct option is A $R_d=\sqrt{2}{R}_p$

$\frac{m{v}^2}{R}=qvB$.For proton $R_p=\frac{mv}{qB}=\frac{\sqrt{2m_{p}E}}{qB}$
and for deutron $R_d=\frac{\sqrt{2m_{d}E}}{qB}$
$\Rightarrow \frac{R_d}{R_p}=\sqrt{\frac{m_d}{m_p}}=\sqrt{2}\Rightarrow R_d=\sqrt{2}{R}_p$