A tightly wound solenoid of length 0.60m and cross-sectional area 3.0×10−4m2 has 1800 turns and carries a steady current of 4.0A.
a. (i) Starting from the work done in establishing the current through an inductor, derive an expression for the total magnetic energy stored in this solenoid in terms of its magnetic field B, permeability μ0, and volume.
b. (ii) Hence obtain the expression for energy density of a magnetic field in vacuum.
c. (iii) Using your result from part (i), calculate the energy stored in the solenoid with the given data.