A tightly wound long solenoid carries a current of 15 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 $m_{e}=9 \times 10^{-37} \mathrm{~kg}$, charge of electron $|\mathrm{q}|=1.6 \times 10^{-19} \mathrm{C}$, $\left.\mu_{0}=4 \pi \times 10^{-7} \frac{\mathrm{~N}}{\mathrm{~N}^{2}}, 1 \mathrm{~ns}=10^{-9} \mathrm{~s}\right]$