Magnetic Effects Of Current Question 8
Question 8 - 2024 (29 Jan Shift 2)
Two particles $\mathrm{X}$ and $\mathrm{Y}$ 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 $\mathrm{X}$ and $\mathrm{Y}$ is :
(1) $\left(\frac{R_{2}}{R_{1}}\right)^{2}$
(2) $\left(\frac{R_{1}}{R_{2}}\right)^{2}$
(3) $\left(\frac{R_{1}}{R_{2}}\right)$
(4) $\left(\frac{R_{2}}{R_{1}}\right)$
Show Answer
Answer: (2)
Solution:
$R=\frac{\mathrm{mv}}{\mathrm{qB}}=\frac{\mathrm{p}}{\mathrm{qB}}=\frac{\sqrt{2 \mathrm{~m}(\mathrm{KE})}}{\mathrm{qB}}=\frac{\sqrt{2 \mathrm{mqV}}}{\mathrm{qB}}$
$\mathrm{R} \propto \sqrt{\mathrm{m}}$
$\mathrm{m} \propto \mathrm{R}^{2}$
$\frac{\mathrm{m}{1}}{\mathrm{~m}{2}}=\left(\frac{\mathrm{R}{1}}{\mathrm{R}{2}}\right)^{2}$
