Question

Each of the following particles is projected with the same speed into a uniform magnetic field $B$ such that the particle's initial velocity is perpendicular to $B$. Which one would move in a circular path with the largest radius?

A particle is projected at a given speed into a uniform magnetic field B and perpendicular to it. Choose the particle that will have the largest radius.

• A. Proton
• B. Beta particle
• C. Alpha particle
• D. Electron
• E. Positron

Answer 1

The correct option is C Alpha particle

Radius of circular path $r=\frac{mv}{Bq}$

$⟹$ $r=k\frac{m}{q}$ where $k=\frac{v}{B}=constant$

For proton : $r_p=k\frac{m_p}{q}$

For alpha particle :$m_{\alpha }=4m_p$ ; $q_{\alpha }=2q$

$\therefore$ $r_{\alpha }=k\frac{4m_p}{2q}=2k\frac{m_p}{q}$

For beta particle, electron and positron : $m^{\prime }=\frac{m_p}{1836}$;$q^{\prime }=q$

$\therefore$ $r^{\prime }=k\frac{m_p}{1836q}$

$⟹$ $r_{\alpha }$ $>r_p>r^{\prime }$

Thus radius of circular path is largest for the alpha particle.