Magnetic fields within a toroid inductor.

[MileHigh]

Now suppose that you have a toroid.  Let's say that there are 100 turns and there is one ampere flowing through the wire.

As you walk around the in the center horizontal plane of the toroid, you are "seeing" 100 wires with upwards current and 100 wires with downwards current.  So you would expect that as you walk around the loop the summation will be zero net current.

Now, in the previous example you got a zero net current summation as you walked around the loop.  But depending on where you were there was a measurable magnetic field.  Sometimes it pointed left, sometimes it pointed right.

Here is the biggie:  The 100 + 100 wires that are emanating a magnetic field are all perfectly symmetrical.  The wire spacing is all evenly spread out.  You have symmetry.

Because there is symmetry in the physical layout of the wires, you are never closer to an particular "upwards" wire or a particular "downwards" wire.

Therefore you know that the field that you see as you walk around the toroid MUST be the same in all places because of the symmetry.

At the same time you know that the net current seen by the loop is 100 up + 100 down which equals zero net current.

Put those two concepts together:   The field must be the same everywhere and the summation of the field x walking through the circle must be zero.

The only magnetic field condition that will satisfy both of those requirements at the same time is for the magnetic field to be ZERO everywhere in the horizontal plane of the toroid.

This same set of conditions will apply if you are outside the toroid or if you are inside the "doughnut hole" of the toroid.

Inside the toroid itself is a different story, and in this thread we already showed what the magnetic field looks like inside the toroid.

MileHigh

[xee2]

Very important point:   Even though the summation is zero, the magnetic field is not necessarily zero in this two-wire example as you walk around the loop.

Yes. When the sum of the fields is zero, both fields are still present. Just because the net field strength at some point is zero, it does not mean that there is no magnetic field at that point. It only means you can not detect the field at that point. The fields do not magically disappear, they are still there. I see many text books saying that the magnetic field "disappears" and that is not true.

[xee2]

Because there is symmetry in the physical layout of the wires, you are never closer to an particular "upwards" wire or a particular "downwards" wire.

MileHigh

You lost me there. The distance to any particular wire will change as you move (unless you move in a circle around it).

[tinman]

I think i may have found a time lag in the magnetic field,from the outer part of the core,to the inner part of the core-or something like that???
Ok,we have a toroid core with three windings of equal length and wire size raped around the toroid core.1 is our primary,and the other two are the secondaries.Each secondary has a 100 ohm load resistor across it. Using an ac input to the primary,is it possable to get a phase shift between the two secondaries? from 0* right through to 180* out,simply by raising the frequency?.

[xee2]

I think i may have found a time lag in the magnetic field,from the outer part of the core,to the inner part of the core-or something like that???
Ok,we have a toroid core with three windings of equal length and wire size raped around the toroid core.1 is our primary,and the other two are the secondaries.Each secondary has a 100 ohm load resistor across it. Using an ac input to the primary,is it possable to get a phase shift between the two secondaries? from 0* right through to 180* out,simply by raising the frequency?.

My first guess would be no. Both secondaries are driven by the same flux path circulating in the toroid and therefore will have the same output if they are identical. However, if the primary is next to one of the secondaries, then it is possible that there is capacitive coupling between that secondary and the primary which does not exist for the other secondary. This creates a more complex circuit which may produce a difference in phase shift between the two secondaries. Are you actually seeing this? Does it happen when the primary is not near the secondary coils? Do the secondaries have a different capacitance to ground? As the frequency is increased, even very small (often unnoticed) capacitances will create all sorts of funny problems in ccircuits. That is why professional engineers are very careful to avoid stray capacitance.