A tightly wound long solenoid carries a current of \( 1.5 \, \text{A} \). An electron is executing uniform circular motion inside the solenoid with a time period of \( 75 \, \text{ns} \). The number of turns per metre in the solenoid is ________.
[Take mass of electron \( m_e = 9 \times 10^{-31} \, \text{kg} \), charge of electron \( |q_e| = 1.6 \times 10^{-19} \, \text{C} \), \( \mu_0 = 4\pi \times 10^{-7} \, \frac{N}{A^{2}} \), \( 1 \, \text{ns} = 10^{-9} \, \text{s} \)]
