recently I am working on magnetic solenoid and got a question. The attachment shows the simple cross-section. Blue green represents the steel providing the magnetic flux path and red is the copper wire with current flowing into the screen. Also, the whole structure is in cylindrical shape. It is like rotating the cross-section in the attachment with the axis of the left line 360 degree. A1=2A2. According to magnetic circuit theory, magnetic flux is on the left part of the steel should be approximately two times of the one on the other parts of the steel. Since B=phi/A, H=B/mu, and A1=2A2, magnetic field intensity is the same everywhere. Am I right? What I confused is I believe the root cause of the magnetic field is the current. If we calculate H using the Biot-Savart law, How can H be the same at the whole path of the steel? Also, does saturation in the steel generate more loss compared to the situation without saturation? I read it from my colleague's report and I couldnt figure it out. I only read about hysteresis loss. Thank you for your help.