Question
A tightly wound long solenoid carries a current of
1.5 A. An electron is executing uniform circular motion inside the solenoid with a time period of 75 ns . The number of turns per metre in the solenoid is __________ .
[Take mass of electron $m _e=9 \times 10^{31} kg$, charge of electron $\left| q _e\right|=1.6 \times 10^{-19} C$,$
\left.\mu_{o}=4 \pi \times 10^{-7} \frac{N}{A^2}, 1 ns=10^{-9} s\right]
$

Answer

(250)
Sol. Since time period of a revolving charge is $\frac{2 \pi m}{ qB }$
Where $B =$ magnetic field
$
\begin{array}{l}
\text { due to a solenoid }=\mu_0 nI \\
\therefore T=\frac{2 \pi m}{q\left(\mu_0 nI\right)} \\
75 \times 10^{-9}=\frac{(2 \pi)\left(9 \times 10^{-31}\right)}{1.6 \times 10^{-19} \times 4 \pi \times 10^{-7} \times n \times 1.5} \\
N=250
\end{array}
$

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