# Somewhat confused as to the basis for Ampere-Turn

#### SamR

Joined Mar 19, 2019
1,621
@crutschow to quote you "An ampere-turn, as the name implies, is simply one ampere going through one coil turn. It is independent of the wire size or the coil diameter. Thus, for example, two amperes flowing through 100 turns would be 200 ampere-turns."

OK, I should just take that at face value which only leaves out that it is in a vacuum. Since this is an electromagnetive force or also stated as magnetomotive force I am confused as to the "independent of the wire size or the coil diameter" part. Not so much the diameter but size and spacing between loops (to be specific length ie circumference). How does this not affect the force generated? The Ampere has no length associated with it but Turns would seem to imply a circumference length. It seems obvious to me that the longer the wire the more force being generated? I don't have a problem with the density of force/area but the actual force itself? I know this is going to get into some math above my ability but an explanation I can understand would be helpful. Thx Sam

#### AlbertHall

Joined Jun 4, 2014
8,998
'Turns' is a dimensionless number bearing no relation to the size of the coil.

#### SamR

Joined Mar 19, 2019
1,621
I understand that but why wouldn't a larger/longer turn exert more force?

#### crutschow

Joined Mar 14, 2008
24,062
I understand that but why wouldn't a larger/longer turn exert more force?
It may or may not.
Ampere-turns is only one factor determining the magnetic field intensity, which does vary with coil size, wire spacing, and magnetic permeability of the surrounding medium.

#### AlbertHall

Joined Jun 4, 2014
8,998
I understand that but why wouldn't a larger/longer turn exert more force?
Because it is more spaced out?

#### Jony130

Joined Feb 17, 2009
5,126

#### SamR

Joined Mar 19, 2019
1,621
Thx Jony I scanned the material but will take some time to digest it. But I think this answers my question. Let me chew on it for a while and I'll be back with my synopsis.

#### SamR

Joined Mar 19, 2019
1,621
OK, so Magnetomotive Force Fm has multiple definitions with only one of several being AmpTurns.

Fm= I x N (Ampere x #Turns)

Fm= 2 W / Φ (Joules/Webers)

Fm= Φ × Rm (Weber x Reluctance)

Fm= H × le (Field strength (ampere/meter) x effective Length)

So while ampere turns does not denote force it does indeed contain force in its conversion to other units. This will take a while to gel.

Thx guys! Sam

#### MrAl

Joined Jun 17, 2014
6,945
Humans find ways to simplify things so that they can deal with them easier and faster.
Often multi dimensional problems are reduced to just one dimension when possible. That
is because one dimensional problems are easier to understand and often help to make
calculations easier. This usually requires some added assumptions which are usually
no longer stated once the simplifications becomes commonplace because it is assumed that
the underlying concepts are understood within the context of the problems that come up.
This is unfortunate because it means it makes learning more difficult, but then again
it is also hard to keep stating the same things over and over again for each and every
small problem that comes up.

When it comes to F=N*I the assumption is that the entire field lies within the boundaries
of the area or space being considered, and the area being considered is usually the cross
sectional area of the magnetic path. However, even that is often simplified so that we can
think of the entire field as being at the axial center of the coil. This means that there
is no fringing and thus no loss of flux, so that all of the flux participates in the magnetic
circuit. So everything physical about the problem is reduced from three dimensions down to
just one or two.

As an example, we can look at the relationship between an electical circuit and a magnetic
circuit. A simple electric circuit is a constant voltage source in series with two resistors,
R1 and R2, which themselves are both in series. The total resistance R is R1+R2 and the
current is given by Ohm's Law:
I=E/R
or solving for E we get:
E=I*R
So the electromotive force is equal to the current times the resistance.

Now a magnetic circuit has a coil usually with a magnetically active metal core. The metal core
has high permeability so most of the field is contained within the core. The magnetomotive force
then can be simplified to N*I where N is the number of turns and I is the DC electrical current.
Since this creates a flux Phi in a reluctance R, we can write:
Fm=Phi*R
and Fm=N*I.
Now if the core has an air gap the reluctance Rg is separate from the reluctance of the core Rc
and we have again:
Fm=Phi*R
where R=Rg+Rc the total reluctance of the core and air gap combined.

So we can see how using Fm=N*I can simplify things. The other assumption is that the core has
high permeability but that is not always mentioned or that the total reluctance is known.

Another way of looking at it is that N*I is really the force but in a given local region it may be less unless there is something that can concentrate the force all in one region which of course means all of the flux participates in the intended purpose.

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