Question

Two particles of equal charges after being accelerated through the same potential difference enter in a uniform transverse magnetic field and describe circular paths of radii $R_1$ and $R_2$. Then the ratio of their respective masses $\left(M_1/M_2\right)$ is

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

Answer 1

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

From energy conservation;

$qv=\frac{1}{2}M{v}^2$ or $v=\sqrt{\frac{2qV}{M}}$ .........(i)

And $Bqv=\frac{M{v}^2}{R}$ or $Bq=\frac{Mv}{R}=\frac{M}{R}\sqrt{\frac{2qV}{M}}=\frac{\sqrt{2qVM}}{R}$ (Using (i))

or $M=\frac{B^2{q}^2{R}^2}{2qV}=\frac{B^{2}q{R}^2}{2V}$

$\therefore M\propto R^2$ ($\therefore$ B,q and V are same for the given two particles)

Hence, $\frac{M_1}{M_2}={\left(\frac{R_1}{R_2}\right)}^2$