Appeared in: 2026 (2 sets)
A charged particle +q in an electric field $\vec{E}$ experiences a force in the direction of the electric field. As a result, its kinetic energy changes. Similarly, the charged particle also experiences a force when it moves in a magnetic field $\vec{B}$. But this magnetic force is perpendicular to both velocity $\vec{v}$ of the charged particle and the magnetic field $\vec{B}$, so it cannot change the kinetic energy of the charged particle. Consider two charged particles 1 and 2 of masses m and $\frac{\text{m}}{2}$ having charges -q and +2q respectively. They are accelerated from rest through the same potential difference V and acquire kinetic energy $K_1$ and $K_2$. Then they enter in a region of uniform magnetic field $\vec{B}$ perpendicular to their velocities. (i) The ratio of their kinetic energies $\left(\frac{K_1}{K_2}\right)$ is : (A) $\frac{1}{2}$ (B) $\frac{1}{4}$ (C) 4 (D) 1