A solenoid of length ℓ and uniform cross-sectional area A has N tightly wound turns and is air-cored.
a. (i) Starting with the expression for the magnetic field inside the solenoid, derive a formula for its self-inductance L in terms of μ0,N,A and ℓ.
b. (ii) A solenoid 0.40m long with radius 2.0cm has 2000 turns. Calculate its inductance for an air core.
c. (iii) The solenoid is now completely filled with a material of relative permeability μr=100. Find the new inductance and determine the ratio of the magnetic energy stored in the solenoid for a current of 1.0A with and without the core.