First slide

Force on a charged particle moving in a magnetic field

Question

Two particles X and Y having equal charges, after being accelerated through the same potential difference, enter a region of uniform magnetic field and describes circular path of radius R₁ and R₂, respectively. The ratio of mass of X to that of Y is

Moderate

A

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

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

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

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

Solution

$r = \frac{\sqrt{2 mk}}{qB} = \frac{1}{B} \sqrt{\frac{2 mV}{q}} \Rightarrow r \propto \sqrt{m} \Rightarrow \frac{m_{1}}{m_{2}} = {(\frac{R_{1}}{R_{2}})}^{2}$

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