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…

A tightly wound long solenoid carries a current of $\displaystyle 1.5$ A. An electron is executing uniform circular motion inside the solenoid with a time period of $\displaystyle 75$ ns . The number of turns per metre in the solenoid is $\displaystyle \_\_\_\_$. [Take mass of electron $\displaystyle \mathrm{m}_{\mathrm{e}}=9 \times 10^{-31} \mathrm{~kg}$, charge of electron $\displaystyle \left|\mathrm{q}_{\mathrm{e}}\right|=1.6 \times 10^{-19} \mathrm{C}$, $$\left.\mu_0=4 \pi \times 10^{-7} \frac{\mathrm{~N}}{\mathrm{~A}^2}, 1 \mathrm{~ns}=10^{-9} \mathrm{~s}\right] $$