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 elec

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 $| q_{e} |$ $= 1.6 \times 10^{- 19} C, μ_{0} = 4 π \times 10^{- 7} \frac{N}{A^{2}}, 1 ns = 10^{- 9} s$ ] [2025]

Smart Achievers · Accepted Answer

(250)

Since time period of a revolving charge is $\frac{2 π m}{q B}$

Where B = magnetic field

Due to a solenoid B = $μ_{0} n I$

$\Rightarrow \frac{2 π m}{q T} = μ_{0} n I$

$\Rightarrow n = \frac{2 π m}{q T μ_{0} I}$

$= \frac{2 π \times 9 \times 10^{- 31}}{1.6 \times 10^{- 19} \times 75 \times 10^{- 9} \times 4 π \times 10^{- 7} \times 1.5}$

$\Rightarrow n = \frac{9 \times 10^{- 31}}{1.6 \times 10^{- 19} \times 75 \times 10^{- 9} \times 2 \times 10^{- 7} \times 1.5}$

$\Rightarrow n = \frac{9 \times 10^{4}}{360} = 250$ per meter

Solution

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Solution

Ans. (250) Since time period of a revolving charge is 2πmqB Where B = magnetic field Due to a solenoid B = μ0nI ⇒ 2πmqT=μ0nI ⇒ n=2πmqTμ0I =2π×9×10–311.6×10–19×75×10–9×4π×10–7×1.5 ⇒ n=9×10–311.6×10–19×75×10–9×2×10–7×1.5 ⇒ n=9×104360=250 per meter

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