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  4. An electron gun is placed inside a long solenoid of radius R on its axis. The solenoid has 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) :

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Q. An electron gun is placed inside a long solenoid of radius $R$ on its axis. The solenoid has $n$ 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) :Physics Question Image

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Solution:

Top view of solenoid
Maximum possible radius of electron $= \frac{R}{2}$
$\therefore \frac{R}{2} = \frac{mv}{qB} = \frac{mv_{max}}{e\left(\mu_{0}ni\right)}$
$v_{max} = \frac{R}{2} \frac{e\,\mu _{0}ni}{m}$

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