# Saturation of an iron core?

Lets assume we have a 1 kg iron core, and a 100 kg iron core. Now saturation is defined as how much that core can absorb the magnetic field, since they are different sizes, don't they saturate at different fields?

Lets assume the 1kg core saturates at 1 Tesla, shouldn't the larger core saturate at a higher magnetic field?

Now saturation is defined as how much that core can absorb the magnetic field

Not quite. The saturation point of a ferromagnetic is roughly defined as the internal $\mathbf{B}$-field strength at which ferromagnetic amplification of the external $\mathbf{H}$-field stops. It doesn't really have anything to do with the size of the material.

A crude way of thinking of ferromagnetic materials is that (ignoring magnetic hysteresis) they act like "amplifiers" of external magnetic fields. This amplification factor is given by the relative permeability $\mu_r$; for example, iron typically has an amplification factor of 4000, meaning that it amplifies an externally-applied $\mathbf{H}$-field by a factor of 4000 relative to vacuum.

Unfortunately, this amplification stops past a certain point, typically on the order of several Tesla. This means that if $\mathbf{B}=\mu_r\mathbf{H}=2\text{Tesla}$ is the saturation maximum of the material, then increasing $\mathbf{H}$ by a factor of 2 will NOT result in $\mathbf{B}=4\text{Tesla}$, but in fact will be much less, maybe 2.1 Tesla.

One thing that does confuse me as far as the effect of size is concerned is this line on the Wiki page:

Saturation limits the maximum magnetic fields achievable in ferromagnetic-core electromagnets and transformers to around 2 T, which puts a limit on the minimum size of their cores.

Does anyone know what is meant when they say it puts a limit on the minimum core size?

• Ah, I assumed that if the ferromagnet is large, the saturation of the ferromagnet would be at stronger fields. Thanks for the answer! – Pupil Mar 9 '14 at 21:31
• But I wonder, if $B$ was under 1 $Tesla$, wouldn't the iron core easily increase it to over a $Tesla$? – Pupil Mar 9 '14 at 21:54
• Minimum core size: Generally, for a given power/current/etc level of a transformer design, the smaller it is, the higher the magnetic field in the core. (More specifically, the magnetic field of a solenoid goes as the current times the number of windings per unit length along the coil.) So if you want to keep the field below saturation, you will have to use a larger core (more specifically, a longer coil) than you would for a higher field. – DMPalmer Jun 11 '18 at 19:26

I think as written above the maximum flux density of a material is limited to 2 tesla in a transformer so we can find out the magnetic filed strength for a flux density of 2 tesla so from it we can find out area of core for which we will get flux density of 2 tesla.

But if we reduce the area of core less than that particular value then as flux density is limited to 2 tesla the decrease in area will not increase flux density but will cause higher iron losses and higher magnetising current and lower power factor so we can say that it limits the minimum size of transformer

It is easier to see B and H like a circuit. B is equivalent to current density, H is equivalent to voltage drops per unit travel. Permeability is the conductivity per unit travel. So for a unit cross section, voltage drop per unit travel * conductivity per unit travel =current. Imaging the conductivity (permeability) is not a constant value but a function of voltage (H). When it reaches saturation, the iron core conductivity to magnetic flux diminishes from a very high value to that of air. The energy stored per unit volume = Voltage (H) per unit travel * current density (B) * per unit cross section. When reaches saturation, your magnetic circuit has much lower conductivity, therefore, when applying the same extra potential (Ampere-Turns), not much flux or energy increase.

So it is all about the property of volume density. A larger volume does not give you higher property density.

• Welcome on Physics SE and thank you for your contribution :) You might want to see this page for typesetting formulas – Sanya Oct 28 '16 at 16:01

As once the core get saturated ( maximum flux density of core of transformer is 1.7 tesla) then further increase in magnetic field intensity, there is no change in flux density which implies it is worthless to increase the size once we have reaches the level of core saturation.

H - strength of the magnetic field. B - how dense magnetic field lines are packed within in a magnetically permeable material. B = µ0µrH = magnetic permeability times magnetic field strength. The equation didn't include size of the core, therefore magnetic field density isn't measured by its size. 1kg of iron will have the same magnetic field saturation as 100kg of iron as long as they are made of the same material, no matter the size. Wikipedia was wrong about bigger cores having higher levels of saturation.

The reason why generators etc are large, well because of magnetic flux, which is determined by size of the core. Flux = magnetic field density times the area of the core, pertaining to the number of magnetic field lines in a given area. The bigger the core, the more flux, but that doesn't mean saturation and field density changes their value.

The way that the maximum flux density and core area determines the minimum size of the core is that the product of flux density and core area determines the number of turns needed to obtain a given voltage.

If you could double the saturation field, it would be possible to use either half as many turns in the transformer, which would require a smaller winding window, or half the core area. (Note that doubling the frequency has the same effect as doubling the magnetic field on the number of turns needed to induce a given voltage.)

Additionally, the cross sectional area of the copper wire determines the IxIxR loss. The IxIxR losses in the copper turns and the eddy current losses in the magnetic core determine the size of the core needed to dissipate the heating caused by the losses. The higher the required power, and thus current, the larger the area of copper wire is needed. Again, this determines the size of the winding window and thus of the magnetic core volume that is needed.

Ultimately, minimizing the losses and the heat rise is what determines the size of the core. I am a retired electronic design engineer.