Details:
Background information (1):
The electric power transformer is a remarkably simple (zero moving parts) and efficient device (often better than 95%). Its job is equally simple, to convert alternating-current electric power from one voltage/amperage ratio to a different voltage/ amperage ratio. See, total electric power is measured in watts, which generally can be thought of as being the product of volts and amperes. So, 1000watts can equal 10V x 100A, or it can equal 10000V x .1A. Transformers let us convert either to the other (or to still other combinations of volts and amperes). The reason we want to do this is because all ordinary electric wires have resistance to the flow of electric current, and this resistance causes energy to be wasted. But current is measured in amperes, so the less current, the less resistance and the less wastage. Thus we use transformers to convert power into minimal flows of current, so that it can be sent long-distance with minimal losses. However, since the associated high voltages are difficult to handle safely in such places as homes and factories, more transformers are used to lower the voltages at those locations. In this case the power losses are still minor, because relatively short distances of wire are used between transformers and electric-powered devices. "Modern civilization", which is literally DEFINED by its widespread usage of electricity, depends utterly upon transformers. Nevertheless, if you think about the Grand Total of electric power generation, and realize that just about all of it goes through at least two transformers, their combined inefficiency wasting perhaps 9% of electricity (100% - (95.4% x 95.4%)), well, you can see that even-more-efficient power transformers would be a Good Thing. (I arbitrarily chose 95.4% as being "better than 95%".)

Background information (2):
As stated in the Synopsis, most of the power losses inside a transformer are caused by hysteresis, which is a physical property of magnetic materials (such as the iron cores of transformers). It is a resistance to any change in direction of the orientation of a magnetic field in the material. Consider a simple electromagnet, which is just a nail and a coil of wire: One end of the nail will become a North magetic pole, and the other end of the nail will become a South magnetic pole. For this to happen, inside the nail, tiny regions known as "magnetic domains", which are normally oriented in random directions, must be re-oriented so that a significant percentage of them are aligned in the same direction. Keep in mind that magnetic domains are pieces of solid matter that are surrounded by other pieces of solid matter! Is it any wonder that there is resistance to such re-orientations? Now imagine forcing the North and South magnetic poles of that nail to swap places, 50 or 60 times per second! The world's electric power is mostly generated as Alternating Current, at 50 or 60 cycles per second (nationality-dependent), because transformers only work with A.C. power. (If this sounds like a Catch-22, well, just remember that Direct Current power losses over long distances through ordinary wiring will add up to lots more than only 9%.) Workers in this industry refer to a magnetic material as being "hard" or "soft", as a way of describing its hysteresis characteristics. The most efficient transformer cores are magnetically "soft", with minimal hysteresis.

Background information (3):
It should be mentioned that it is not essential to use iron to make an electromagnet. The coil of wire all by iself qualifies. However, the strength of the magnetic field is usually vastly weaker without the nail, than with the nail. (If one uses a big enough coil and plenty of Amperes, then the iron is not necessary -- but "big enough coil" means a LOT of wire, and "plenty of Amperes" means lots of electrical resistance. That's as wasteful or even more wasteful than hysteresis.) What the nail offers to an electromagnet is an "amplification" effect among the magnetic domains inside the iron. If you've ever played with a couple of bar magnets on a tabletop, you may have tried pushing one around with the other. This is a little tough to do for a significant distance, because the magnet being pushed will often spin around so that it is attracted to instead of repelled by the magnet you were holding/pushing-with. Well, the same thing happens at the level of magnetic domains: When the electromagnet coil first causes some of the domains to become aligned, they push other magnetic domains around, causing them to become aligned also. All the domains that become aligned (but many do not become aligned) will contribute to the total field of the electromagnet. Yet there is a bit of a paradox here. Permanent magnets are made from magnetically "hard" materials, and the "harder" they are, the stronger fields they have. In those materials, almost every single magnetic domain has been forced into alignment -- and they stay there because of the material's "hardness". (There may also be a difference at the atomic level, regarding the number of electrons-per-atom that contribute to the magnetic properties of the material.) "Soft" materials usually manage to leave quite a few domains unaligned, so electromagnets often have to be rather energy-consumptive to be as strong as permanent magnets. Ideally then, we'd like to have transformer cores that have maximal "hardness" per magnetic domain, but easily allows ALL its domains to flip....

Background Information (4):
A "ferrofluid" is a mixture of particles of some magnetic material (often iron oxide in the form of magnetite) with a very viscous substance like soft wax (often it is NOT wax per se, but I shall use "wax" here in the generic sense). The magnetic particles are "suspended" in the wax, much like muddy water has dirt suspended in it. In the case of muddy water, when the water is still and not swirling, then because water has low viscosity (flows easily), the dirt particles eventually fall out of suspension, leaving fairly pure water behind. Depending on the kind of dirt, this sort of thing COULD happen to dirty motor oil, but it will take quite a while for the dirt to fall out of suspension because motor oil is more viscous than water. With some really viscous stuff like wax, particles can stay in suspension for a long long time, indeed! --Well, it depends on the particle, of course. As you know, iron is fairly heavy stuff, about eight times heavier than an equal volume of water. If you could suspend particles of pure iron in the water, without it immediately rusting, then the iron would fall out of suspension quite a bit more quickly than dirt. Similarly, magnetite and not iron is used in ferrofluids, because the density of magnetite is only a little more than 5 times that of water (and again any iron would rust, while magnetite can be called "already rusted iron"). Ferrofluids are packed full as much as possible with iron oxide, which makes the wax more of a "matrix", than a "suspendor". Ferrofluids are kind of putty-like, and exhibit some rather fun behaviours in the presense of magnets. They FLOW toward magnets like some kind of life-form, exuding a psuedopod.... Ferrofluids have also been hideously expensive, partly because of the actual substance of the "wax", and partly because of the effort put into grinding the magnetite particles into incredibly fine dust (which makes suspension easier, of course). A reference I found says, "First developed for NASA in the 1960’s, ferrofluids are tiny magnetised metal particles in an oil suspension. They have now found specialised uses in a variety of specialised applications, from loudspeakers to rotary seals - but in relatively small quantities." That last is because of the hideous expense, of course -- but that first part, is mistaken about "magnetised metal particles"; NASA scientists were working with magnetite. Recently the price of ferrofluids has been dropping, possibly due to the good old supply/demand chicken/egg thing (prices go down as production goes up; but production only goes up to meet demand, which does NOT go up much when faced with high prices!). It could be the popularity of ferrofluid-based speakers, because they produce high-quality sound, thanks to the simple fact that ferrofluids exhibit practically ZERO hysteresis, and so can easily be used in conjunction with Alternating Currents of thousands of times per second...("audio frequencies").

At Last!, the Idea:
Above, the guy who got that description wrong, about what ferrofluids are, actually got it right with respect to what we need for electric-power transformer cores (and I was quite surprised to see that error, too!). Magnetite particles are FAR weaker in magnetic intensity, than filings from ground-up permanent magnets! And I did write, "Ideally then, we'd like to have transformer cores that have maximal "hardness" per magnetic domain, but easily allows ALL its domains to flip...."

Each particle of magnetic material in a ferrofluid is the same as a magnetic domain, and the suspendor- oil can simply be seen as a lubricant, allowing the domains to easily flip. All we need is a box (tough and nonmagnetic), shaped like a transformer core, filled with ferrofluid.

I especially want to repeat that this transformer-core ferrofluid should use the same magnetically hard material as is found in permanent magnets (there are many, so pick a relatively inexpensive one, that is corrosion-resistant). This material does need to be ground into powder, but I'm going to suggest that we use the same sort of "grinding" systems that are used to manufacture ball bearings -- basically huge rotating drums full of non-round bearings and grinding dust --we just run those grinders a whole lot longer. That way we get enormous quantities (inexpensive!) of tiny spherical magnetic domains (use magnets to separate them from the grinding dust, of course), which will indeed flip extremely easily when mixed with oil, and have near-zero hysteresis.

Transformer efficiency will likely jump to 99%. That wasted-power formula which I presented earlier then becomes 100% - (99% x 99%), or 2%. So, if every existing high-power transformer was replaced with a ferrofluid-core transformer, we would gain back 7% of presently-wasted electricity, for real usage, with zero new power-plant construction. I say it's worth doing!