A toroidal solenoid has a mean radius r and a cross-sectional area A and is wound uniformly with N1 turns. A second toroidal solenoid with N2 turns is wound uniformly around the first. The two coils are wound in the same direction. Part A. Derive an expression for the inductance L1 when only the first coil is used.
Part B. Derive an expression for the inductance L2 when only the second coil is used.
Part C. Find the mutual inductance of these solenoids M.

Asheet of steel 1.5 mm thick has nitrogen atmospheres on both sides at 1200oc and is permitted to achieve a steady-state diffusion condition. the diffusion coefficient for nitrogen in steel at this temperature is 6 x 10- 11 m2 /s, and the diffusion flux is found to be 1.2 x 10-7 kg/m2 -s. also, it is known that the concentration of nitrogen in the steel at the high-pressure surface is 4 kg/m3 . how far into the sheet from this high-pressure side will the concentration be 2.0 kg/m3 ? assume a linear concentration profile.