# integral and simple forms of Ampere's law

Discussion in 'Homework Help' started by PG1995, May 18, 2012.

Apr 15, 2011
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2. ### steveb Senior Member

Jul 3, 2008
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The two pronounciations I've heard are bye-oh sav- vahr and bee-oh sav- ahr. I'm not sure which is perfectly correct.

For your other question. The simplified formula assumes that the H vector is parallel to the dl vector, and that the magnitude of the H vector is constant over the path length of integration.

If you had a case where the H vector had constant magnitude, but was not parallel and always maintained a constant angle, then you could augment the simple formula by multiplying by the cosine of the angle.

Last edited: May 18, 2012
3. ### PG1995 Thread Starter Active Member

Apr 15, 2011
753
5
Thank you.

H=Ni/lc, where "N" is number of turns, "i" is current and "lc" is mean core length.

To me, it looks that H would always be constant because current enters one way and the same current exits the other way and the numbers of turns won't change neither would lc. Then, what would make the magnitude of H non-constant over the path of integration? Please help me with it. Thank you.

Regards
PG

4. ### steveb Senior Member

Jul 3, 2008
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469
The path of integration is something you choose. Whether or not it is possible to choose a path that has H constant or nearly constant (in the sense that I defined above) is determined by geometrical symmetry. Usually it is not possible to find such a path, but in some simple cases it is possible. The simplest case is an infinitely long wire with current flowing. The H vector goes around the wire circularly, and the magnitude of H goes down the farther away you get. If you define a crazy/wild path around the wire, you will not have H constant. However, if you choose perfect circles around the wire (with the wire at the center), then Ampere's law can be used for a circle of any radius. There are very few other cases where you have symmetry, but when you use iron cores to direct the magnetic fields, then you can sometimes approximate a symmetrical path, or at least simplify the path into sections that you can assume to have constant H, such as your example.

Keep in mind that flux and H are different, and for H to be constant around a path through the core, the core would need to have constant cross sectional area.