An iron core is inserted into a solenoid 0.5 m long with 400 turns per unit length. The area of cross-section of the solenoid is `0.001m^(2)`. (a) Find the relative permeability of the core when a current of 5 A flows through the solenoid winding. Under these conditions, the magnetic flux through the cross-section of the solenoid is `1.6xx10^(-3)` Wb. (b) Find the inductance of the solenoid under these conditions.