1. Dec 20, 2012

CheyenneXia

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.

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Last edited: Dec 20, 2012
2. Dec 20, 2012

Enthalpy

Because of the rotation symmetry, the cross area at left is not twice that at right. Good design would put the same cross area everywhere, so iron gets a uniform induction; it could well be your case.

Biot-Savart works without iron only - and for simple shapes...

In real life, forget everything differential. Compute the reluctance from the magnetic path's length, permeability... and deduce the induction and flux. Stick to these circuit global figures.

Saturation itself doesn't create iron losses. Iron losses increases with the induction nearly squared. Saturation can prevent your part work properly (but is sometimes desired: fluxgate magnetometers, magnetic amplifiers, pulse generators...). Say, a transformer can't resist the primary voltage any more when its core saturates, and then the current increases exaggerately.

3. Dec 24, 2012

CheyenneXia

You are right. The cross area at left is not twice of the right after rotating. It is not the real design. I just use this drawing for my questions.

I went back to the book and the internet. I only got the info that Biot-Savart works for magnetostatic case. Other than that, not much. Do not take it wrong. It is not that I do not believe you that it doesnt work with iron. I just want to learn more about it.

When you say "Iron losses increases with the induction nearly squared", do you mean the eddy loss?

Coincidently I am reading a book related to electrical machines and i am on the transformer charpter. Excitation current and primary current really confuse me. I posted my question here

Also, I didnt get why saturated core generates exaggerately larger current. When the core is saturated, should emf which is related to dphi/dt be reduced?

4. Dec 25, 2012

Enthalpy

Biot&Savart won't work, because at some places you have a magnetic material and at some others none.

Hysteresis losses increase more or less as the induction squared, too.

When the core is saturated, dphi/dt is limited by phi, so the primary can't respond to the external voltage by the emf, and all the excess external voltage creates a current limited only by ohmic loss. Since coil and transformer designs want small ohmic losses, the current can increase a lot when the core saturates.