Question 188 of 276
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 , charge of electron ,
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Answer: 250
Since time period of a revolving charge is
Where magnetic field
due to a solenoid
$\begin{aligned}
& \therefore \mathrm{T}=\frac{2 \pi \mathrm{~m}}{\mathrm{q}\left(\mu_0 \mathrm{nI}\right)} \\
& 75 \times 10^{-9}=\frac{(2 \pi)\left(9 \times 10^{-31}\right)}{1.6 \times 10^{-19} \times 4 \pi \times 10^{-7} \times \mathrm{n} \times 1.5} \\
& \mathrm{~N}=250
\end{aligned}$
Where magnetic field
due to a solenoid
$\begin{aligned}
& \therefore \mathrm{T}=\frac{2 \pi \mathrm{~m}}{\mathrm{q}\left(\mu_0 \mathrm{nI}\right)} \\
& 75 \times 10^{-9}=\frac{(2 \pi)\left(9 \times 10^{-31}\right)}{1.6 \times 10^{-19} \times 4 \pi \times 10^{-7} \times \mathrm{n} \times 1.5} \\
& \mathrm{~N}=250
\end{aligned}$
