How Does the Length of a Yoke Affect the Inductance of Yoked Coils in Series?

[Phaedrus]

When finding for "L" is the value for "l" (length of coil) affected by the length of the core material. Or more specifically when one is working this equation for two coils yoked in series do you figure each coil separately?...and if NOT, do you include the length of the yoke?
Here is a link to the equation in question...http://sub.allaboutcircuits.com/images/10237.png"

I usually have pretty good luck finding this stuff on my own but I have a heck of a time finding anything out about yoked coils. Any search words or anything to point me in the right direction would be greatly appreciated.

 

[Bob S]

See section on "Inductance of solenoid" in

http://en.wikipedia.org/wiki/Solenoid

If you put two N-turn solenoids end-to-end on the same core and put the two coils in series, you double the number of turns, double the length, and double the inductance.

Bob S

 

[Phaedrus]

Hey thanks...I kinda figured that would be the case if they were put together end to end. What I'm hoping to determine is how do you treat length when they are yoked in series. Is the yoke included in the length?...What I'm am looking at is basically a horseshoe electro magnet, with the coils wrapped on each end connected in series.
Hope that helps.

 

[Bob S]

Hey thanks...I kinda figured that would be the case if they were put together end to end. What I'm hoping to determine is how do you treat length when they are yoked in series. Is the yoke included in the length?...What I'm am looking at is basically a horseshoe electro magnet, with the coils wrapped on each end connected in series.
Hope that helps.

For an iron dominated horseshoe magnet, the flux between the two coils is contained within the iron, so the two coils are magnetically in series. The formula for the magnetic field doesn't work so well however, because the high "reluctance" of the air gap between the two ends dominates the magnetic properties. See

http://sci-toys.com/scitoys/scitoys/magnets/calculating/calculating.html

Also Google magnetic reluctance air gap

Bob S

 

[Phaedrus]

I guess I don't see how that relates to two coils yoked together where they are next to each other pointed up with a yoke across the bottom...like a U.

From what I understand the lines of flux would be completely different if the ends faced each other as opposed to parallel to each other. With a parallel configuration we should get a nice big rainbow arch, whereas facing each other we would just have a bubble between the ends.

 

[Bob S]

I guess I don't see how that relates to two coils yoked together where they are next to each other pointed up with a yoke across the bottom...like a U.

From what I understand the lines of flux would be completely different if the ends faced each other as opposed to parallel to each other. With a parallel configuration we should get a nice big rainbow arch, whereas facing each other we would just have a bubble between the ends.

In a "U" yoke, if you follow the flux through the iron from one coil to the other, the two coils are (in high permeability iron) linked with high inductive coupling (at very low frequency) independent on exactly where the two coils are located on the horseshoe.

In this case, the high air-gap reluctance at the open end of the "U" completely determines the inductance. If all the flux is contained within the iron, then one coil can be slid along the iron to the other end of the horseshoe without loss of coupling or change of inductance. In actuality, the two coils should be as close to the air gap (open end) as possible.

The air gap at the open end of the "U" nearly completely determines the magnetic and electrical characteristics of the "U" magnet. 1 cm of air gap has the same reluctance as about 10 meters of soft iron. The (low frequency) inductance will be very dependent on the presence of any ferrous material in the air gap. Any conductive metal sheet in the air gap will increase the real part of the magnet impedance, decreasing the ac inductance and increasing ac losses.

Bob S