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

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 the masses of X to that of Y is-

TestHub · Accepted Answer

The kinetic energy gained by a charged particle accelerated through a potential difference $V$ is $K E = q V$ .

Also, $K E = \frac{1}{2} m v^{2}$ , so $q V = \frac{1}{2} m v^{2}$ .

The radius of the circular path in a magnetic field $B$ is $R = \frac{m v}{qB}$ .

From $R = \frac{m v}{qB}$ , we get $v = \frac{qBR}{m}$ .

Substituting $v$ into the kinetic energy equation:

$q V = \frac{1}{2} m (\frac{qBR}{m})^{2} = \frac{1}{2} m \frac{q ^{2} B ^{2} R ^{2}}{m ^{2}} = \frac{q ^{2} B ^{2} R ^{2}}{2 m}$ .

Rearranging for mass $m$ :

$m = \frac{q B ^{2} R ^{2}}{2 V}$ .

Since $q$ , $B$ , and $V$ are the same for both particles, $m \propto R^{2}$ .

Therefore, $\frac{m _{X}}{m _{Y}} = (\frac{R _{1}}{R _{2}})^{2}$ .

Physics - Magnetism Question with Solution | TestHub

Options:

Doubts & Discussion

JEE Main (2028)