AIIMS 2018 Physics Motion of Charged Particles in Magnetic Field MCQ Question

In a uniform magnetic field, the radius $r$ of the circular motion of a charged particle is given by the equation $r = \frac{mv}{qB}$, where $m$ is the mass, $v$ is the velocity, $q$ is the charge, and $B$ is the magnetic field strength. For a deuteron (mass $m_d$ and charge $q_d = e$) and an α particle (mass $m_\alpha = 4m_d$ and charge $q_\alpha = 2e$), both moving in the same radius $r$, their kinetic energies can be expressed as $E_d = \frac{1}{2} m_d v_d^2$ and $E_\alpha = \frac{1}{2} m_\alpha v_\alpha^2$. Since the radius is the same, the velocities adjust such that $v_\alpha = \frac{m_d}{m_\alpha} v_d$, leading to $E_\alpha = E_d$, confirming that the energy of the α particle is equal to that of the deuteron, $E_\alpha = E_0$.

Options B (2E₀), C (E₀/2), and D (E₀/4) are incorrect because they imply a different relationship between mass, charge, and energy that does not hold true under the