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 \(m_{e}=9 \times 10^{-31} \mathrm{~kg}\), charge of electron \(\left|\mathrm{q}_{\mathrm{e}}\right|=1.6 \times 10^{-19} \ \mathrm{C}\),

\(\left.\mu_{0}=4 \pi \times 10^{-7} \frac{\mathrm{~N}}{\mathrm{~A}^{2}}, 1 \mathrm{~ns}=10^{-9} \mathrm{~s}\right]\)

Answer 1

Answer is : 250

Since time period of a revolving charge is \(\frac{2 \pi m}{\mathrm{qB}}\) 

Where B = magnetic field

due to a solenoid = \(\mu_0nI\) 

\(\therefore \ T = \frac{2\pi m}{q(\mu_0nI)}\) 

\(75 \times 10^{-9}=\frac{(2 \pi)\left(9 \times 10^{-31}\right)}{1.6 \times 10^{-19} \times 4 \pi \times 10^{-7} \times n \times 1.5}\) 

\(\mathrm{N}=250\)