Rankers Physics

Force Acting on Moving Charges: Practice Problem & Solution

A proton and an alpha particle both enter a region of uniform magnetic field, $B$, moving at right angles to the field $B$. If the radius of circular orbits for both the particles is equal and the kinetic energy acquired by proton is $1\text{ MeV}$, the energy acquired by the alpha particle will be: (2015 Pre)
$1\text{ MeV}$
$4\text{ MeV}$
$0.5\text{ MeV}$
$1.5\text{ MeV}$

Solution Explained:

To solve this problem, we apply the core principles of Force Acting on Moving Charges. Understanding the underlying formula is key to arriving at the correct answer below:

Radius is $r = \frac{\sqrt{2mK}}{qB}$. For equal radii, $K \propto \frac{q^2}{m}$. Since $q_\alpha = 2q_p$ and $m_\alpha = 4m_p$, the kinetic energy remains $1\text{ MeV}$.

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