Question

Two particles of equal charges after being accelerated through the same potential difference enter a uniform transverse magnetic field and describe circular path of radii $ {{R}_{1}} $ and $ {{R}_{2}} $ respectively. Then the ratio of their masses $ ({{M}_{1}}/{{M}_{2}}) $ is

• A. $ \frac{{{R}_{1}}}{{{R}_{2}}} $
• B. $ {{\left( \frac{{{R}_{1}}}{{{R}_{2}}} \right)}^{2}} $
• C. $ \frac{{{R}_{2}}}{{{R}_{1}}} $
• D. $ {{\left( \frac{{{R}_{2}}}{{{R}_{1}}} \right)}^{2}} $
• E. $ {{\left( \frac{{{R}_{1}}}{{{R}_{2}}} \right)}^{1/2}} $

Answer 1

Answer: (B)

Radius of circular path
$ R=\frac{mv}{qB} $ but $ mv=\sqrt{2mqV} $
$ \therefore $ $ R=\frac{\sqrt{2mqV}}{qB} $
Or $ R\propto \sqrt{m} $
Or $ \frac{R_{1}^{2}}{R_{2}^{2}}=\frac{{{M}_{1}}}{{{M}_{2}}} $
Or $ \frac{{{M}_{1}}}{{{M}_{2}}}=\frac{R_{1}^{2}}{R_{2}^{2}}={{\left( \frac{{{R}_{1}}}{{{R}_{2}}} \right)}^{2}} $