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 describe circular paths of radii $R_1$ and $R_2$, respectively. The ratio of masses of $X$ and $Y$ is

• A. $(R_1/R_2{)}^{1/2}$
• B. $\left(R_2/R_1\right)$
• C. $(R_1/R_2{)}^2$
• D. $\left(R_1/R_2\right)$

Answer 1

The correct option is C $(R_1/R_2{)}^2$

When a charge particle is allowed to move in a uniform magnetic field, then it described spiral or circular path
Centripetal force, $\frac{m{v}^2}{R}=qvB\therefore v=\left(\frac{qB}{m}R\right)$
Hence, $\sqrt{\frac{2qV}{m}}=\left(\frac{qB}{m}\right)R[\because V=\sqrt{\frac{2qV}{m}}]$
$\Rightarrow R={\left(\frac{2mV}{q}\right)}^{1/2}\times \frac{1}{B}$
or, $m\propto R^2[\because V,q$ and $B$ are constant]
or, $\frac{m_1}{m_2}={\left(\frac{R_1}{R_2}\right)}^2$.