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  • Two charged particles X and Y after being accelerated through the same potential difference V, enter a region of uniform magnetic field B and describe circular paths of radii r1

Two charged particles X and Y after being accelerated through the same potential difference V, enter a region of uniform magnetic field B and describe circular paths of radii r1 and r2 respectively. Then the ratio
\mathrm{\frac{\text { charge to mass ratio of } X}{\text { charge to mass ratio of } Y}, ~is}.

Option: 1

\mathrm{\left(\frac{r_1}{r_2}\right)^{1 / 2}}


Option: 2

\mathrm{\left(\frac{r_1}{r_2}\right)}


Option: 3

\mathrm{\left(\frac{r_1}{r_2}\right)^2}


Option: 4

\mathrm{\left(\frac{r_2}{r_1}\right)^2}


Answers (1)

best_answer

\mathrm{ r=\frac{\sqrt{2 m q V}}{q B}=\frac{1}{B}\left(\frac{2 m V}{q}\right)^{1 / 2} \\ }

\mathrm{ \therefore \quad \frac{q}{m}=\frac{2 V}{B^2 r^2} \\ }

\mathrm{\therefore \quad \frac{\left(\frac{q}{m}\right)_X}{\left(\frac{q}{m}\right)_Y}=\left(\frac{r_2}{r_1}\right)^2 \quad }       (\because B and V are the same)
So the correct choice is (d).

Posted by

Rishabh

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