JEE MAIN - Physics (2025 - 7th April Morning Shift - No. 7)
A particle of charge $q$, mass $m$ and kinetic energy $E$ enters in magnetic field perpendicular to its velocity and undergoes a circular arc of radius (r). Which of the following curves represents the variation of $r$ with $E$ ?
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Explanation
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$$\begin{aligned} & \frac{\mathrm{mv}^2}{\mathrm{r}}=\mathrm{qvB} \\ & \mathrm{mv}=\mathrm{qBr} \\ & \mathrm{E}=\frac{1}{2} \mathrm{mv}^2 \\ & \mathrm{E}=\frac{1}{2} \mathrm{~m}\left(\frac{\mathrm{q}^2 \mathrm{~B}^2 \mathrm{r}^2}{\mathrm{~m}^2}\right)=\frac{\mathrm{q}^2 \mathrm{~B}^2 \mathrm{r}^2}{2 \mathrm{~m}} \\ & \mathrm{E}=\left(\frac{\mathrm{q}^2 \mathrm{~B}^2}{2 \mathrm{~m}}\right) \mathrm{r}^2 \\ & \mathrm{r}^2 \propto \mathrm{E} \end{aligned}$$
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