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My understanding of the theory is:

Some devices (e.g.motors) generate harmonic frequency currents & radio interference.

Add a ferrite core: the oscillating current generates magnetic flux; ditto eddy currents; ditto heat.
So the core will absorb energy from the wire, if correctly designed it will absorb most strongly in
the most damaging frequencies.

But every core I have seen is wrapped round the whole cable. So the negative current in Neutral
cancels the positive current in Live, so no flux or eddies or heat. I have even seen cores on DC
power supplies: how much radio energy will a DC supply generate?

Apologies if I have got it completely wrong. I cannot find any clear explanation how these cores
are supposed to work. Do they actually do anything or are they just fashion accessories?
Thank you
 
There are lots of different applications for ferrite cores, but the ones used for RFI suppression of cables leaving equipment are installed as you say, around the whole cable. The point is that the radiated interference they are there to tackle is not in the form of a current flowing around the intended circuit which, as you correctly point out, they will have negligible effect on because the two legs of the circuit cancel each others' MMF in the core. However, much RFI is common-mode, using the cable as an antenna versus (for example) the case of the appliance as a ground plane. The entire cable, all conductors in parallel, act like the telescopic antenna of a portable radio, which is not a circuit in itself but becomes one when the ground plane of the radio innards is taken into account. Threading the ferrite onto the cable provides common-mode inductance, which chokes the RFI trying to leave the equipment, without altering the (intended) differential-mode signals passing along the cable.

Many DC power supplies are switched-mode, which rectify the mains, chop it up into pulses with very fast rise times, transform them and rectify again. The chopping and rectifying can produce lots of RF, not least because of the amount of power involved. This could appear, for example, as common mode on the DC output relative to the AC input and radiate from both cables, hence one or both might benefit from a ferrite.

As with all RFI control measures, ferrites work best as part of an engineered scheme, rather than just plonked on the cable at random. They (and the cable through them) behave as genuine electronic components at the frequencies under consideration with calculable inductance, resonance, Q etc.
 
I'd also add to Lucien's excellent answer that different formulations of ferrites have different permeability and loss tangent as a function of frequency, - which boils down in practical terms to varying ability to attenuate different frequencies which you might be interested in attenuating.

It's worth bearing in mind that when purchasing low-grade combinations of switch mode power supplies (LED drivers) which you might interconnect to various "raw" led products in the form of LED strips, LED tile lights, or just garden variety MR16 bulbs, then you are constructing an untested combination. It's entirely likely that a budget-import-unbranded etc LED driver might have had "some" testing against limits in an anechoic chamber, and might even come out with a "CE" mark accordingly. - But the methodology of the test might not exclude the manufacturer from conveniently fitting ferrites to the input and output test cables during their testing process, under the argument that they are testing "only" the driver. - What goes on down the cables connecting it is not part of their problem.
Meanwhile you buy the ACME LED driver, convinced by the CE mark, and connect is to several metres of cables and some MR16 bulbs or led strip, and all of a sudden the customers digital radio or wifi craps out.
 

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