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Rutherford's Experiment and Observations

Two charged p...

Question

Two charged particles having charges $q_{1}$ and $q_{2}$ and masses $m_{1}$ and $m_{2}$ are projected with same velocity in a region of uniform magnetic field. They follow the trajectory as shown in figure. From this, we can conclude that-

A

\frac{m_{1}}{q_{1}} < \frac{m_{2}}{q_{2}}

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B

\frac{m_{1}}{q_{1}} > \frac{m_{2}}{q_{2}}

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C

m_{2} < m_{1}

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D

q_{1} < q_{2}

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Solution

The correct option is A $\frac{m_{1}}{q_{1}} < \frac{m_{2}}{q_{2}}$
From the figure, it is clear that $R_{1} < R_{2}$

Radius of circular path traced by charge particle in a uniform magnetic field is,

$R = \frac{m v}{q B}$

$\Rightarrow R \propto \frac{m}{q}$

$∴ \frac{m_{1}}{q_{1}} < \frac{m_{2}}{q_{2}}$

Hence, $(A)$ is the correct answer.

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