Question

An electron is shot into one end of a solenoid at the speed of 800 m/s making an angle $30°$ with the axis of solenoid. Current in solenoid is 4 A and there are total 8000 turns over solenoid. If the total number of revolutions made by electron within solenoid before emerging from another end of solenoid is $n\times {10}^6$, then the value of n is
$\left(\frac{e}{m}=\sqrt{3}\times {10}^{11}\text{C/kg (write two digits after the decimal point.)}\right]$

Answer 1

$B={\mu }_0{n}_{1}i={\mu }_0\frac{8000}{l}i$
$T=\frac{2\pi m}{eB}\&t=\frac{l}{v\cos \theta }$

$t=NT$
$\frac{l}{v\cos \theta }$= $N\times \frac{2\pi m}{e}\frac{l}{{\mu }_0\times 8000\times i}$
$N=\frac{e}{m}\frac{{\mu }_0\times 8000\times 4}{800\times \frac{\sqrt{3}}{2}\times 2\pi }$
$=1.6\times {10}^6$