First slide

Force on a charged particle moving in a magnetic field

Question

Mixed He⁺ and O²⁺ions (mass of He⁺ = 4 amu and that of O²⁺ = 16 amu) beam passes a region of constant perpendicular magnetic field. If kinetic energies of all the ions are the same, then

Moderate

A

He⁺ ions will be deflected more than those of O²⁺
B

He⁺ ions will be deflected less than those of O²⁺
C

All the ions will be deflected equally
D

No ions will be deflected

Solution

$\begin{array}{l} r = \frac{\sqrt{2 mK}}{qB} \Rightarrow r \propto \frac{\sqrt{m}}{q} \Rightarrow \frac{r_{{He}^{+}}}{r_{O^{+ +}}} = \sqrt{\frac{m_{{He}^{+}}}{m_{O^{+ +}}}} \times \frac{q_{O^{+ +}}}{q_{{He}^{+}}} \\ = \sqrt{\frac{4}{16}} \times \frac{2}{1} = \frac{1}{1} . They will deflect equally . \end{array}$

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