Two particles X and Y having equal charges are being accelerated through the same potential difference. Thereafter, they enter normally in a region of uniform magnetic field and describes circular pat

Question

Two particles X and Y having equal charges are being accelerated through the same potential difference. Thereafter, they enter normally in a region of uniform magnetic field and describes circular paths of radii R 1 and R 2 respectively. The mass ratio of X and Y is :

TestHub · Accepted Answer

Energy gained due to potential difference by charged particle:

$K E = q V$

Relation between momentum & kinetic energy:

$p = \sqrt{2 m (K E)}$

Now, radius of the circular path under magnetic field will be given by,

$R = \frac{m v}{q B} = \frac{p}{q B} = \frac{\sqrt{2 m (K E)}}{q B} = \frac{\sqrt{2 m q V}}{q B}$

Therefore,

$R \propto \sqrt{m} \Rightarrow m \propto R^{2}$

$\Rightarrow \frac{m_{1}}{m_{2}} = {(\frac{R_{1}}{R_{2}})}^{2}$

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