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 $\ldots\ldots$ -. [Take mass of electron $\mathrm{m}_{\mathrm{e}}=9 imes 10^{-31}…

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 $\ldots\ldots$ -.
[Take mass of electron $\mathrm{m}_{\mathrm{e}}=9 \times 10^{-31} \mathrm{~kg}$, charge of electron $\left|\mathrm{q}_{\mathrm{e}}\right|=1.6 \times 10^{-19} \mathrm{C}$,
$\left.\mu_0=4 \pi \times 10^{-7} \frac{\mathrm{~N}}{\mathrm{~A}^2}, 1 \mathrm{~ns}=10^{-9} \mathrm{~s}\right]$

Aicharya · Accepted Answer

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

A tightly wound long solenoid carries a current of 1.5 A. An electron is executing uniform circular motion…

Solution