Question:
An electron gun is placed inside a long solenoid of radius $R$ 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):
Correct Option: , 2
Solution:
(2) Magnetic field inside the solenoid is given by
$B=\mu_{0} n I$
Here, $n=$ number of turns per unit length
The path of charge particle is circular. The maximum
possible radius of electron $=\frac{R}{2}$
$\therefore \quad \frac{m V_{\max }}{q B}=\frac{R}{2}$
$\Rightarrow V_{\max }=\frac{q B R}{2 m}=\frac{e R \mu_{0} n I}{2 m}$