Magnetic fields within a toroid inductor.

[MileHigh]

Xee2:

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.

If the net field strength is zero, then there is no magnetic field at that point.  Look at the case of the two wires example, one with current flowing downwards and the other with current flowing upwards.  There will be zero net field when the magnetic field vector due to each wire is equal in strength and they are 180 degrees apart in direction.

A little complication that may be worth mentioning is that when you walk around the loop and do the summation you are only looking at the part of the magnetic field that's in the same direction that you are moving.  Look at the original clip where he says something like "the dot product can be ignored because the direction of integration and the direction of the magnetic field are always in the same direction."   He intentionally keeps it simple where the magnetic field is always in the same direction as the movement.

What this means is that in the two-wire example you can have net zero field in the direction of your tangential movement which contributes zero to your summation, but there still could be a "radial" magnetic field.  You don't worry about the possible "radial" component of the net magnetic field due to the two wires.  You travel in your circle and add up the magnetic field components that are in the same (or 180 degree opposite) direction that you are traveling.  I may have made things too complicated, so I don't know if I am helping or hindering.

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

I think I may be able to explain this one without complicating things too much.  Let's suppose the toroid has 360 turns.  You are standing on your circle outside the toroid and you are going to take your walk around the loop.  The circle you are going to walk on is centered on the center of the toroid and the toroid has perfect symmetry.

So you are looking at the toroid.  Then you move one degree along your circular path to the right.  What do you see?  You see the toroid and it looks exactly the same.  You move ten degrees along the path and you look at the toroid, it still looks exactly the same.  The distance between you and each wire of the toroid that cuts the center plane is always the same when you look at the wires as a whole set.  So if the toroid looks exactly the same from any angle, then the magnetic field MUST be the same at any point along the circle.  If you do the same thing on a circle with a larger radius, the same type of thing happens.

So you know that the magnetic field must always be the same as you go around the circular path because of symmetry.  You also know that the summation of your magnetic field times your movement must be zero amperes.  Certainly your movement in meters is not zero, therefore the magnetic field strength must be zero everywhere outside the toroid for everything to make sense and add up properly.

So that also means if just one loop of the toroid is larger than all the others and sticks out, then the symmetry is broken and now there will be an observable magnetic field everywhere outside the toroid.  That's why you say that a real-life toroid that you make on your bench will have a "near zero" magnetic field outside the doughnut shape, because it's impossible to build a toroid with perfect symmetry.

MileHigh

[MileHigh]

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?.

A component like a transformer will only work properly below a certain frequency.  So it's not surprising that you see the phase shift change as you increase the frequency.  However, there should be a certain bandwidth where the transformer does its job properly.  The phase shift could be due to capacitive and other effects.  If you Google something like "AC characteristics of a transformer" or "frequency response of a transformer" you should get tons of hits.

As a side note and not related to this discussion, the classic mechanical equivalent for a transformer is simply a set of two gears.  If you look at the rotational speed and torque characteristics of a set of gears they are identical to the voltages and currents associated with an electrical transformer.

MileHigh

[xee2]

If the net field strength is zero, then there is no magnetic field at that point. 

I greatly respect your opinions, but I do disagree with you on this (and I know many agree with your position, so I may be the odd man out).
If you have a space filled with multiple magnetic field generators, as you move about the space there may be places where the magnetic field strength goes to zero. If the magnetic fields actually disappeared, then where did the energy in the magnetic field go? The only reasonable answer, is that the fields and their energy are always there. It is only measured strength that goes to zero. Back when I started in electronic engineering (a long time ago) we used slot lines (which are slots cut in wave guide) with a probe to measure the e-field strength inside the wave guide as a way of determining microwave frequency. If the signal really disappeared when the e-field went to zero there would be no wave coming out the end of the wave guide (but there was). I feel that teaching that the field disappears creates a lot of confusion about what is really happening.

[tinman]

Well at these high frequencies,probably nothing out of the ordinary then, But here is the experiment anyway.
First i cast two half toriod cores ,using liquid steel. Perm not so god,but still quite magnetic. I then wound one of the secondaries around one half of the toroid core. I then glued the two halves together. So now we have the secondaries windings passing through the middle of the core.

Once dry,i then wound the primary and the second secondairy around the whole core-as per normal.All wires were of equal length. It's a bit rough,but was only for a quick experiment.
Sorry the volume is a bit low,but it was filmed at 1am,and everyone was asleep.

http://www.youtube.com/watch?v=_C1VC_-f3Z0

[xee2]

So that also means if just one loop of the toroid is larger than all the others and sticks out, then the symmetry is broken and now there will be an observable magnetic field everywhere outside the toroid.  That's why you say that a real-life toroid that you make on your bench will have a "near zero" magnetic field outside the doughnut shape, because it's impossible to build a toroid with perfect symmetry.

MileHigh

Nice explanation.