First slide

Force on a charged particle moving in a magnetic field

Question

The charge on a particle Y is double the charge on particle X. These two particles X and Y after being accelerated through the same potential difference enter a region of uniform magnetic field and describe circular paths of radii R₁ and R₂ , respectively. The ratio of the mass of X to
that of Y is

Moderate

A

${(\frac{2 R_{1}}{R_{2}})}^{2}$
B

${(\frac{R_{1}}{2 R_{2}})}^{2}$
C

$\frac{R_{1}^{2}}{2 R_{2}^{2}}$
D

$\frac{2 R_{1}^{}}{R_{2}^{}}$

Solution

$\begin{array}{l} r = \frac{1}{B} \sqrt{\frac{2 mV}{q}} \Rightarrow r \propto \sqrt{\frac{m}{q}} \Rightarrow \frac{r_{x}}{r_{y}} \times \sqrt{\frac{m_{x}}{q_{x}} \times \frac{q_{y}}{m_{y}}} \\ (∵ K = qV) \\ \Rightarrow \frac{R_{1}}{R_{2}} = \sqrt{\frac{m_{x}}{m_{y}} \times \frac{2}{1}} \Rightarrow \frac{m_{x}}{m_{y}} = \frac{R_{1}^{2}}{2 R_{2}^{2}} \end{array}$

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