3) Nonlinear Consider two coaxial solenoids shown at the left. The inner ferromagnetic solenoid has height of 20 cm, radius of R1 = 0.2 cm, and N1 = 200 turns. The outer solenoid has height of 10 cm, radius of R2 = 0.4 i2 cm, and N2 = 50 turns. Between solenoids, there is nonmagnetic material with µ. = 1 (if you want you can take it as air). The material inside the inner solenoid is a nonlinear ferromagnetic material, whose Brotal VS. H curve is given below. A current of i1 = 8 mA flows clockwise direction at inner solenoid, and a current of Nonmagnetic material i2 = 12 mA flows counterclockwise direction at outer solenoid. By ignoring edge-effects for both solenoids and assuming very long solenoids (so the fields at the center points can be taken same with the fields at the edge points), Btotal (T), Slope = 500µo -7 H (A/m) a) Calculate the self-inductances (L1 and L2), mutual inductance (M) between solenoids, and total magnetic energy stored in the system. b) If the currents are half of the values given above, compare inductance values (greater? smaller? same?) with the ones that you have found in part a). Is total stored magnetic energy quarter of the value that you have found in part a)? Explain. Make qualitative explanations as much as possible.

3) Nonlinear Consider two coaxial solenoids shown at the left. The inner ferromagnetic solenoid has height of 20 cm, radius of R1 = 0.2 cm, and N1 = 200 turns. The outer solenoid has height of 10 cm, radius of R2 = 0.4 i2 cm, and N2 = 50 turns. Between solenoids, there is nonmagnetic material with µ. = 1 (if you want you can take it as air). The material inside the inner solenoid is a nonlinear ferromagnetic material, whose Brotal VS. H curve is given below. A current of i1 = 8 mA flows clockwise direction at inner solenoid, and a current of Nonmagnetic material i2 = 12 mA flows counterclockwise direction at outer solenoid. By ignoring edge-effects for both solenoids and assuming very long solenoids (so the fields at the center points can be taken same with the fields at the edge points), Btotal (T), Slope = 500µo -7 H (A/m) a) Calculate the self-inductances (L1 and L2), mutual inductance (M) between solenoids, and total magnetic energy stored in the system. b) If the currents are half of the values given above, compare inductance values (greater? smaller? same?) with the ones that you have found in part a). Is total stored magnetic energy quarter of the value that you have found in part a)? Explain. Make qualitative explanations as much as possible.