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4.Moving Charges and Magnetism
medium
Two particles $x$ and $y$ have equal charges and possessing equal kinetic energy enter in a uniform magnetic field and describe circular path of radius of curvature $r_1$ and $r_2$ respectively. The ratio of their masses is
A
$\left( {\frac{{{r_1}}}{{{r_2}}}} \right)$
B
${\left( {\frac{{{r_1}}}{{{r_2}}}} \right)^{1/2}}$
C
${\left( {\frac{{{r_1}}}{{{r_2}}}} \right)^2}$
D
${\left( {\frac{{{r_2}}}{{{r_1}}}} \right)}$
Solution
$\mathrm{r}=\frac{\sqrt{2 \mathrm{mE}_{\mathrm{k}}}}{\mathrm{qB}}$
$\mathrm{r} \propto \sqrt{\mathrm{m}} \quad\left(\mathrm{q}, \mathrm{B}, \mathrm{E}_{\mathrm{k}} \rightarrow \text { same }\right)$
or $m$ $ \propto $ $r^{2}$
$\frac{m_{1}}{m_{2}}=\left(\frac{r_{1}}{r_{2}}\right)^{2}$
Standard 12
Physics