Target Exam

CUET

Subject

Physics

Chapter

Moving Charges and Magnetism

Question:

Proton, deuteron and alpha particles of same kinetic energy are moving in circular trajectories in a constant magnetic field. The radii of proton, deuteron and alpha particle are respectively $r_p, r_d$, and $r_α$. Which one of the following relation is correct?

Options:

$r_α=r_p=r_d$

$r_α=r_p<r_d$

$r_α>r_p>r_d$

$r_α=r_p>r_d$

Correct Answer:

$r_α=r_p<r_d$

Explanation:

$R = \frac{mv}{qB} = \frac{\sqrt {2mE}}{qB}$

$ R_p =  \frac{\sqrt {2m_pE}}{eB}$

$ R_\alpha =  \frac{\sqrt {2(4m_p)E}}{2eB} = \frac{\sqrt {2m_pE}}{eB} = R_p$

$ R_d =  \frac{\sqrt {2(2m_p)E}}{eB} = \frac{\sqrt {4m_pE}}{eB} > R_p$

$\Rightarrow R_p = R_\alpha < R_d$