To construct a solenoid having cross-sectional area \(1.256 \times 10^{-3} \mathrm{~m}^{2}\) and 500 windings that can produce a magnetic field of \(10 \times 10^{-3} \mathrm{~T},\) 

(a) calculate the length of the solenoid if the current in the device is \(5 \mathrm{~A}\). 

(b) Calculate the inductance of the solenoid,

(c) considering the cross-sectional area and given magnetic field, the amount of magnetic potential energy stored in the solenoid.

(d) Using the value of \(L\) obtained in part \((b)\) estimate the magnetic potential energy stored within the solenoid.