Verified Solution • 2025–26 Session moderate

QJEEM25Ph005c: JEE Main 2025 Physics - Class 12 JEEM25Ph005c Solution: A tightly wound long solenoid carries a current of 1.5 A . An…

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 me=9×10−31 kg\mathrm{m}_{\mathrm{e}}=9 \times 10^{-31} \mathrm{~kg} , charge of electron ∣qe∣=1.6×10−19C\left|\mathrm{q}_{\mathrm{e}}\right|=1.6 \times 10^{-19} \mathrm{C} , μ0=4π×10−7 N A2,1 ns=10−9 s]\left.\mu_0=4 \pi \times 10^{-7} \frac{\mathrm{~N}}{\mathrm{~A}^2}, 1 \mathrm{~ns}=10^{-9} \mathrm{~s}\right]

Step-by-Step Verified Solution

Since time period of a revolving charge is 2π mqB\frac{2 \pi \mathrm{~m}}{\mathrm{qB}}

Where B=\mathrm{B}= magnetic field

due to a solenoid =μ0nI=\mu_0 \mathrm{nI}

amp;∴T=2π mq(μ0nI)amp;75×10−9=(2π)(9×10−31)1.6×10−19×4π×10−7×n×1.5amp; N=250\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}

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