An electron gun is placed inside a long solenoid of radius mathrm{R} on its axis. solenoid has mathr

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4.Moving Charges and Magnetism

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An electron gun is placed inside a long solenoid of radius $\mathrm{R}$ on its axis. The solenoid has $\mathrm{n}$ turns/length and carries a current $I$. The electron gun shoots an electron along the radius of the solenoid with speed $v$. If the electron does not hit the surface of the solenoid, maximum possible value of ${v}$ is (all symbols have their standard meaning)

A

$\frac{\mathrm{e} \mu_{0} \mathrm{nIR}}{\mathrm{m}}$

B

$\frac{\mathrm{e} \mu_{0} \mathrm{nIR}}{2 \mathrm{m}}$

C

$\frac{2 \mathrm{e} \mu_{0} \mathrm{nIR}}{\mathrm{m}}$

D

$\frac{\mathrm{e} \mu_{0} \mathrm{nIR}}{4 \mathrm{m}}$

(JEE MAIN-2020)

Solution

Maximum possible radius of electron $=\frac{\mathrm{R}}{2}$

$\therefore \frac{\mathrm{R}}{2}=\frac{\mathrm{mv}}{\mathrm{qB}}=\frac{\mathrm{mv}_{\max }}{\mathrm{e}\left(\mu_{0} \mathrm{ni}\right)}$

$\mathrm{v}_{\max }=\frac{\mathrm{R}}{2} \frac{\mathrm{e} \mu_{0} \mathrm{ni}}{\mathrm{m}}$

Standard 12

Physics

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