Two particles $A$ and $B$ enter a region of uniform magnetic field after being accelerated through the same potential difference. They describe circular paths of radii $4 m$ and $2 m$ respectively. They have the equal charges. Find the ratio of mass $A$ to the mass of $B$

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Detailed Solution

$\begin{array}{l} B q v = \frac{m v^{2}}{R} \to 1, \end{array}$

$e v_{0} = \frac{1}{2} m v^{2} \to 2,$

$R = \frac{m}{B q} \sqrt{\frac{2 e v_{0}}{m}}$

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

$\Rightarrow \frac{m_{1}}{m_{2}} = {(\frac{R_{1}}{R_{2}})}^{2} = 4$

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