MHT CET · Physics · Magnetic Effects of Current

Two particles $X$ and $Y$ having equal charges, are accelerated through the same potential difference. They enter a region of a uniform magnetic field and describe a circular path of radii $r_{1}$ and $r_{2}$ respectively. The ratio of the mass of $X$ to that of $Y$ is

A $\frac{r_{1}}{r_{2}}$
B $\sqrt{\frac{r_{1}}{r_{2}}}$
C ${[\frac{r_{2}}{r_{1}}]}^{2}$
D ${[\frac{r_{1}}{r_{2}}]}^{2}$

Verified Solution

Answer & Solution

Correct Answer

(D) ${[\frac{r_{1}}{r_{2}}]}^{2}$

Step-by-step Solution

Detailed explanation

The force acting on the particle inside the magnetic field is

F_{B} = q v B \sin θ

θ = 90 °

F_{B} = q v B

This provides the necessary centripetal force

F_{c} = \frac{m v^{2}}{r}

∴ \frac{m v^{2}}{r} = q v B \Rightarrow r = \frac{m v}{q B}

= \sqrt{\frac{2 m q V}{q B}}

\frac{r_{1}}{r_{2}} = \sqrt{\frac{m_{x}}{m_{y}}}

\frac{m_{x}}{m_{y}} = {(\frac{r_{1}}{r_{2}})}^{2}

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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Two particles X and Y having equal charges, are accelerated through the same potential difference. They enter a region of a uniform magnetic field and describe a circular path of radii r1 and r2 respectively. The ratio of the mass of X to that of Y is

Step-by-step Solution

Two particles $X$ and $Y$ having equal charges, are accelerated through the same potential difference. They enter a region of a uniform magnetic field and describe a circular path of radii $r_{1}$ and $r_{2}$ respectively. The ratio of the mass of $X$ to that of $Y$ is