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 75ns. The number of turns per metre in the solenoid is_______.
[Take mass of electron me $=9\times {10}^{-31}\mathrm{kg}$, charge of electron $\left|q_s\right|=1.6\times {10}^{-19}\mathrm{C},$ ${\mu }_0=4\pi \times {10}^{-7}\frac{\mathrm{N}}{{\mathrm{A}}^2},1\mathrm{ns}={10}^{-9}\mathrm{s}]$