Magnetic Effects of Current and Magnetism: JEE Main 2025 Physics 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 $m_e = 9\times10^{-31}$ kg, charge of electron $|q_e| = 1.6\times10^{-19}$ C, $\mu_0 = 4\pi\times10^{-7}\ \frac{\text{N}}{\text{A}^2}$, 1 ns $= 10^{-9}$ s]