Physics question about magnetic fields

[daviddeakin]

Given: If a current flows in a straight wire, a certain amount of magnetic flux will be generated around it.

Now suppose I put an iron tube around the wire (but don't change the current). I know the inductance will increase, but is that because more total flux is now being generated, or is the total flux still the same but more of it is now concentrated in the iron, close to the wire, instead of floating around far away in the air as previously?

Putting it another way, I know the flux density close to the wire will increase, but it that because more actual flux is generated or is it because some of the flux in the air has been 'sucked up' into the iron instead (so the flux density in the air has been reduced -a trade from one place to the other)?

[G8HQP Dave]

The H field is set by the current. The induced voltage (which sets the inductance) is set by the B field. The relationship between B and H is set by permeability. So, adding some iron leaves H unchanged but boosts B.

[daviddeakin]

B is flux density, but is the increase in B accomplished because more total flux is now flowing around the conductor (in the iron), or the same total flux but more of it has been diverted away from the edges of the room/universe and instead concentrated into the iron (which is close to the conductor where the flux can do more work) ? I suspect the latter.

[kalee20]

My take on this is that it's because the total flux has increased.

Current flowing in the wire produces a magnetomotive force field, the H field. This is accompanied by the B field, which is dependent on the material.

When current, and fields, change with time, the induced voltage is determined by the B-field. It does not matter exactly where this happens to be, what's important is the total flux surrounding the wire.

Having an iron pipe small diameter, close to the wire makes more difference than a large diameter one farther away, because a path round the wire at a large distance is much longer. So H is less, B is less (you can prove this with a compass or a magnet). But as far as the wire is concerned, the induced voltage is the same for a 1weber field change circling 1cm from the wire as it is for the same field change circling 1km from the wire.

[G8HQP Dave]

As I said, the H field (set by the current) is unchanged. The B field is increased where the iron is. I take that to mean that it is not decreased where the iron isn't.

Think of it another way. Suppose you filled space with iron (or some other way boosted the permeability of free space). You would get increased inductance, yet there would be nowhere for the extra flux to come from because it would be boosted everywhere. Hence it does not have to come from anywhere.

[trobbins]

David, as you deduce, it is the 'latter'.

Further to Dave's post, the total flux doesn't change (iron, or no iron). You may see this in some diagrams that show a representation of flux lines - for example around a single wire, or a transformer winding, or external field lines as they enroach on a microphone transformer (and generate a hum signal). The better the magnetic shield, the more field lines (out of the total number of field lines being generated) are diverted/constrained within the shield. In your example, there would still be some field lines outside a practical iron tube, but their density would be much less than before (ie. any leakage field is much less).

Of course your example is really just a small sectional view of a larger wire loop (through which the current flows) so the distribution of flux lines with distance from the wire will not be uniform in practice in all directions as you move away from the wire.

[daviddeakin]

Thanks everyone, that confirms my suspicions that the the iron works to concentrate more flux where you want it, at the expense of flux density everywhere else, the total flux in the universe remaining the same.

[Radio Wrangler]

If you wind your wire into a tight coil, all of the flux goes through the hole.

Stick a magnetic core through the hole and the inductance goes up. Inductance is the voltage created for a unit of rate of change of current. Lenz' law gives the sign.

If the turns and the diameter are unchanged, then the core must have put up the total flux.

You can model a magnetic circuit like one made of resistors. The battery voltage is the ampere turns in the coil. The current is the flux in any limb. Fix the voltage and reduce the resistance and the current increases.

David

all of the flux goes through the hole.

All the core does is stretch it out so the outside bit has to go further, it will be stronger at the ends in that case. It just concentrates the available flux.

As far as I remember flux = ampere turns with no reference to permeability. Even with a saturated core the total flux is the same, just not where you want it.

[Argus25]

Originally Posted by Radio Wrangler

Inductance is the voltage created for a unit of rate of change of current. Lenz' law gives the sign.

Maybe another way to put that could be that "Inductance is the proportionality constant which relates induced voltage to the rate of change of current..."

One problem that crops up which can confuse the issue is that by this usual definition of induced voltage that contains inductance L, the inductance has its effects related to a rate of change of current with time.

However, if you check the formulas, for example for the inductance of a solenoid, then L = N.(flux)/i (N = number of turns and i current) . This resolves to L = (uo ur N(squared) A )/ l Where A is the cross sectional area and l the length. By this definition there is no time domain parameter and no current specified and it is also obvious if the relative permeability ur is increased, so will the inductance increase. Also if the flux is increased, so the inductance will increase. So it gives more insight into the issue than the formula for the emf of self inductance and it indicates that the effect of the added iron relates both to increasing the flux in the region and increasing ur.

[kalee20]

Originally Posted by daviddeakin

Thanks everyone, that confirms my suspicions that the the iron works to concentrate more flux where you want it, at the expense of flux density everywhere else, the total flux in the universe remaining the same.

No.

If you imagine winding the coil in air, it'll have such-and-such inductance, and a particular field pattern, fading away as you go farther away from the coil.

If you fill your universe with molten iron and let it cool down, the inductance will be vastly increased, but because the iron is EVERYWHERE, the flux density pattern will be the same, just multiplied by a constant of a few thousand at each point in space. So total flux will be increased by this constant.

If you then start milling away the iron, inductance will start to fall gradually - but you could still get to a point of greatly increased inductance, with a tube of iron surrounding the coil. And the total flux linking the coil will still be greater than the air-core case.

[trobbins]

Kalee20, not sure I agree with your molten iron universe outcome. I view that the flux lines nearest the coil will have a higher density due to the iron, but that further away the flux density diminishes quicker - whereby the total flux lines is constant (iron or no iron universes).

[G8HQP Dave]

If increasing local permeability increases flux by stealing it from elsewhere (with the total staying constant, as some seem to believe) then increasing permeability everywhere could not increase flux because there would be nowhere to steal it from. Hence 'iron everywhere' could not have an increased inductance, even if 'iron somewhere' did. This is daft, so it is wrong.

What actually happens is that the iron has its random internal magnets somewhat aligned by the external field so that the total field is increased in the iron. It doesn't steal flux from anywhere else; you actually get two sources of flux: the current and the aligned iron.

Looking at it another way, if the wire plus iron causes less flux to occur away from the iron then it would also be less sensitive to flux changes far away (principle of reciprocity). Hence you would reduce pickup by adding iron. Experience tells us that adding iron increases external pickup.

I suspect that the basic problem here is that the picture of 'lines of flux' taught to all schoolchildren is a useful way of visualising a counter-intuitive phenomenon but it can be misleading if it is taken too seriously. In any case, there is no law of 'conservation of flux'.

[Argus25]

The notion of of magnetic flow or flux was created to analyze "magnetic circuits" in a similar manner to electric ones, where current was equal to electromotive force divided resistance, Ohms Law, so therefore flux was made equal to magnetomotive force or mmf/reluctance. Therefore the magnetic circuit becomes analogous to an electric one.

Reluctance to the flux depends on the magnetic medium (air or metal etc) and the geometry, length and area of the pathway and is equal to the:

cross sectional area x u (the permeability) divided by the path length L. So the notion of flux becomes intrinsically linked with the geometry and properties of the medium, in the same way current in an electric circuit depends on the resistance, which depends on the geometry or length and area and resistivity of the pathway.

However, the mmf is the force generated by a current and is equal to the current I x the number or turns for a solenoid for example and defined also as HL where H is the field intensity and L the length. And this is independent of the magnetic medium.

The H field therefore is the field intensity or mmf/L just as by analogy the electric field intensity is emf/L. So electric force has units of Volts/Meter and magnetic force H is Ampere.Turns/meter.

So combining all of this its easy to see that;

flux = auHL/L = auH

and flux density therefore is flux/a = uH, or B= uH, the famous magnetic equation.

Therefore while H relates to the magnetizing force and is independent of the physical medium, B is not and can be increased by altering the medium, it is not a matter of stealing flux density from anywhere to achieve this.

[daviddeakin]

Originally Posted by G8HQP Dave

If increasing local permeability increases flux by stealing it from elsewhere (with the total staying constant, as some seem to believe) then increasing permeability everywhere could not increase flux because there would be nowhere to steal it from. Hence 'iron everywhere' could not have an increased inductance, even if 'iron somewhere' did. This is daft, so it is wrong.

What actually happens is that the iron has its random internal magnets somewhat aligned by the external field

That makes so much sense. So I can imagine the flux from the internal domains (little permanent magnets) adding to the flux already prodivded by the coil itself?

If the above is true, then do iron and nickel have high permeability because they contain many domains compared with other materials, or stronger domains?

[G8HQP Dave]

Only ferromagnetic materials have magnetic domains. It is a long time since I studied solid state physics so hopefully someone else can answer your question.

[kalee20]

Probably more the latter than the former. Soft iron, when just about fully magnetised, has its domains coalesce, at which point there are very few of them.

There's also the effect that the domains are mobile and able to re-orientate themselves.

Nickel alloys can be very high permeability, but pure nickel is barely attracted to a magnet (try this with a nickel scalpel handle, or an old nickel stirrup).

[ms660]

I've always liked this magnetism demo:

https://www.youtube.com/watch?v=O9DaKP2PhL4

Lawrence.