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. ${{\left( \frac{{{R}_{2}}}{{{R}_{1}}} \right)}^{2}}$

Answer 1

Answer: (B)

${{\left( \frac{{{R}_{1}}}{{{R}_{2}}} \right)}^{2}}$

Answer 2

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 $\frac{{{M}_{1}}}{{{M}_{2}}}=\frac{R_{1}^{2}}{R_{2}^{2}}={{\left( \frac{{{R}_{1}}}{{{R}_{2}}} \right)}^{2}}$