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I come from a biomedical background which has primarily focused on inductors as an element of a transcranial magnetic stimulator. The way this method works is that a copper coil receives pulses of electric current which generates a changing magnetic field. This changing magnetic field is great for getting past the skull and into the brain, where it generates a reverse-direction electric current, used to treat various diseases and malflictions. We don't call these coils "inductors" nor do we call these neural stimulations "eddy currents". But that's probably what you know them as.

I know that typically, inductors use ferromagnets as a core, because they have a much higher saturation level than other materials, leading to higher inductance. However, I have just read that for magnetic stimulation, it is better to use ferrimagnets because they are non-conductive. The book implies that Eddy currents generated in the core of a conductive ferromagnet would weaken the induced electric current in the brain. Is this really true? This is just just conservation of energy I guess? The book seems to assume that there is a layer of insulation between the copper coil and the conductive ferromagnetic center.

Say you have a copper wire that's immersed in a ferromagnetic material - no insulation between the wire and the material. Does the same result apply? Is it because ferromagnets are insulative relative to copper, meaning they won't pick up much current from the actual pulse, but will only pick up the eddy currents?

Now for my real question. Imagine you had a magical material that was uniformly conductive and uniformly ferrimagnetic. Not a conductive wire in a magnetic substance, but a uniformly conductive and magnetizable material, which I guess was also highly conductive like copper. How would the inductance, or induced current, change here?

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  • $\begingroup$ The insulation has no or negligible effect on the inductor. The insulation is placed to avoid unintended electrical contact between the copper wire and the ferromagnetic core. $\endgroup$ – Yashas Jan 26 '17 at 8:08
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Ferrites are non-conductive ferrimagnetic materials with high permeability and high resistance; that makes them very good as the core of an inductor when you want to minimize losses due to eddy currents (conduction in the core).

Large transformers may use laminated ferromagnetic metals (conductors) - you want to use the metals because they are cheap, you laminate (that is, split it into thin sheets of metal that are electrically insulated from each other) in order to disrupt eddy currents / prevent large loops of current from flowing. This helps reduce losses in the core, and thus makes the transformer / inductor more efficient.

Now for my real question. Imagine you had a magical material that was uniformly conductive and uniformly ferrimagnetic. Not a conductive wire in a magnetic substance, but a uniformly conductive and magnetizable material, which I guess was also highly conductive like copper. How would the inductance, or induced current, change here?

A conductive core will generate losses (heat) and reduce the flux linkage (Lenz's law: the current will flow to oppose the changing flux). In the case of a perfect (super) conductor, this effect is such as to prevent any magnetic flux from existing inside (up to certain saturation effects). Whether that material is ferri- or ferro-magnetic will not change the result: if it's a perfect conductor, there will be no flux change inside.

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    $\begingroup$ From the Wikipedia link you posted (in your 1st paragraph), it is mentioned that ferrites are ferrimagnetic, not ferromagnetic. You might want to do a small edit (I won't do it because it changes a bit what you intented to say). $\endgroup$ – thermomagnetic condensed boson Feb 5 '18 at 21:01
  • $\begingroup$ @no_choice99 you are right; I will make some edits. Thanks for pointing it out. $\endgroup$ – Floris Feb 5 '18 at 21:07
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I know that typically, inductors use ferromagnets as a core, because they have a much higher saturation level than other materials, leading to higher inductance. However, I have just read that for magnetic stimulation, it is better to use ferrimagnets because they are non-conductive. The book implies that Eddy currents generated in the core of a conductive ferromagnet would weaken the induced electric current in the brain. Is this really true? This is just conservation of energy I guess? The book seems to assume that there is a layer of insulation between the copper coil and the conductive ferromagnetic center.

Eddy currents are loops of "localized" currents generated in a conductor which arise due to a changing magnetic flux. These loops of current choose the direction of current (clockwise or anticlockwise) such that it opposes the cause of the eddy current.

This video illustrates how magnetic breaking works which is based on the same principle. https://www.youtube.com/watch?v=otu-KV3iH_I

At the end of the video, the author of the video shows a video from the MIT lab. When a perforated copper plate is used, the magnetic breaking is not efficient. The perforated plate has many gaps between the conducting parts. This does not allow efficient circulation of eddy currents. Using a non-conducting or poorly conducting material as the core remove/reduces the effects of eddy current.

We can assume a brain to function like an inductor. Therefore, coupled with your inductor, they behave somewhat like a transformer, i.e: inducing currents in the secondary coil (brain) using the changing flux of the primary coil (your inductor).

Eddy currents are annoying: they produce heat which is a waste of energy and they produce opposing magnetic fields/flux. One way to reduce their effect is as your textbook stated, i.e: to use a poorly conducting material with high susceptibility (ferrite for example).

Another way to reduce eddy currents is by breaking the core into thin sheets and placing a laminating sheet between each of them. However, the function of covering the entire core with an insulating sheet (as you said) is probably to prevent electrical contact between the coil and the core.

Say you have a copper wire that's immersed in a ferromagnetic material - no insulation between the wire and the material. Does the same result apply? Is it because ferromagnets are insulative relative to copper, meaning they won't pick up much current from the actual pulse, but will only pick up the eddy currents?

Ferromagnets having nothing to do with electrical conductivity. They are just a class of magnetic materials.

Now for my real question. Imagine you had a magical material that was uniformly conductive and uniformly ferrimagnetic. Not a conductive wire in a magnetic substance, but a uniformly conductive and magnetizable material, which I guess was also highly conductive like copper. How would the inductance, or induced current, change here?

The more conductive the core is, the more stronger the eddy currents will be. This will reduce the net flux linkage between your inductor and the brain.

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