Physics

Problem

H^+

He^+

and

O^{2+}

all having the same kinetic energy pass through a region in which there is a uniform magnetic field perpendicular to their velocity. The masses of

H^+

He^+

and

O^{2+}

are 1 amu, 4 amu and 16 amu respectively. Then a.

H^+

will be deflected most b.

O^{2+}

will be deflected most c.

He^+

and

O^{2+}

will be deflected equally d. all will be deflected equally

Intuitive explanation

When charged particles move through a perpendicular magnetic field, the magnetic force curves their path into a circle—and the radius depends on both the particle's momentum and its charge. Since all three ions have the same kinetic energy, heavier particles move slower and have smaller momentum, leading to tighter curves. But charge also matters: a higher charge experiences a stronger magnetic force, which also tightens the radius. The key is balancing these two effects using $r = \frac{mv}{qB}$ and the constraint that $KE$ is constant across all three.

Intuitive explanation

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