Two particles X and Y having equal charges, are accelerated through the same potential difference. They enter a region of a uniform magnetic field and describe a circular path of radii r 1 and r 2 res

Question

Two particles X and Y having equal charges, are accelerated through the same potential difference. They enter a region of a uniform magnetic field and describe a circular path of radii r 1 and r 2 respectively. The ratio of the mass of X to that of Y is

TestHub · Accepted Answer

The force acting on the particle inside the magnetic field is $F_{B} = q v B \sin θ$

$θ = 90 °$ , $F_{B} = q v B$

This provides the necessary centripetal force $F_{c} = \frac{m v^{2}}{r}$

$∴ \frac{m v^{2}}{r} = q v B \Rightarrow r = \frac{m v}{q B}$ $= \sqrt{\frac{2 m q V}{q B}}$

$\frac{r_{1}}{r_{2}} = \sqrt{\frac{m_{x}}{m_{y}}}$

$\frac{m_{x}}{m_{y}} = {(\frac{r_{1}}{r_{2}})}^{2}$

Physics - Magnetism Question with Solution | TestHub

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