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My understanding is as follows:

A voltage induces an electric field at a capacitor, which is measured in coulombs. If I wanted the capacitor to leak the charge exponentially, I could model that as a parallel resistor around it.

How would I express the dual of this paragraph for inductors? Something like:

A current induces a magnetic field at an inductor, which is measured in (Webers?). If I wanted the inductor to leak the magnetic flux exponentially, I could model that as a (series resistor?)

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  • \$\begingroup\$ As long as it's not a transformer or something where the leakage from one coil affects another, it might be as simple as putting a resistor in series because the flux is proportional to the current on the wire, and the flux losses are likely proportional to flux density. So, if you're trying to model the losses due to flux leakage, a resistor in series might be your answer. \$\endgroup\$ – K H Aug 7 '18 at 6:35
  • \$\begingroup\$ Yep, looks like you figured it out. \$\endgroup\$ – K H Aug 7 '18 at 6:35
  • \$\begingroup\$ @KH To be honest, I still don't get it. I'm thinking of the water analogy, and how the inductor is like a water wheel. I want to add friction to the water wheel itself. Is that mathematically identical to slowing the water, which turns the wheel? Also, is magnetic field at an inductor measured in Webers? Is electric field at a capacitor measured in coulombs? \$\endgroup\$ – Neil G Aug 7 '18 at 6:38
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    \$\begingroup\$ That's not a bad analogy. Adding resistance in series will cause losses proportional to current, and current happens to be proportional to flux. I know that flux losses depend on physical shape and there are probably some eccentricities to the way flux is lost, but given that those are unknowns without a deep examination, it should be adequate to use a resistor in series for simulation. If you want you can probably use a single resistor to account for all of your losses, flux loss, coil resistance, ringing if present and eddy current losses. \$\endgroup\$ – K H Aug 7 '18 at 6:46
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    \$\begingroup\$ As far as measurement quantities, there are quite a few with regard to magnetics. The Weber is a unit of flux, and flux density is measured in Teslas, so if you have 1 Weber in a cross section of 1 m^2 you have a density of 1 tesla. Coulombs are measurement of charge. 1 Coulomb is 1 Mol (Avogadro's number) of electrons or holes. A capacitor has capacitance rated in Farads, and a capacitance of 1 Farad means that the capacitor can store 1 coulomb of charge per volt it is charged to. The electric field is measured in volts, as basically all a capacitor does is store voltage (pressure) \$\endgroup\$ – K H Aug 7 '18 at 6:51
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As long as it's not a transformer or something where the leakage from one coil affects another, it might be as simple as putting a resistor in series because the flux is proportional to the current on the wire, and the flux losses are likely proportional to flux density. So, if you're trying to model the losses due to flux leakage, a resistor in series might be your answer.

Your waterwheel is not a bad analogy. Adding resistance in series will cause losses proportional to current, and current happens to be proportional to flux. I know that flux losses depend on physical shape and there are probably some eccentricities to the way flux is lost, but given that those are unknowns without a deep examination, it should be adequate to use a resistor in series for simulation. If you want you can probably use a single resistor to account for all of your losses, flux loss, coil resistance, ringing if present and eddy current losses.

As far as measurement quantities, there are quite a few with regard to magnetics. The Weber is a unit of flux, and flux density is measured in Teslas, so if you have 1 Weber in a cross section of 1 m^2 you have a density of 1 tesla. Coulombs are measurement of charge. 1 Coulomb is 1 Mol (Avogadro's number) of electrons or holes. A capacitor has capacitance rated in Farads, and a capacitance of 1 Farad means that the capacitor can store 1 coulomb of charge per volt it is charged to. The electric field is measured in volts, as basically all a capacitor does is store voltage (pressure)

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You would expect a perfect capacitor to store charge when it's open circuited. A leaky capacitor has a large value resistor across its terminals to draw a small current, driven by its terminal voltage. This current reduces the charge stored on the capacitor.

You would expect a perfect inductor to maintain flux when it's short-circuited. A leaky (we usually say 'lossy') inductor has a small value resistor in series to generate a small voltage from this circulating current. This voltage ramps the current down, and with it, the flux.

'Leakage' flux is something else, and is only relevant for transformers. All cored inductors have some flux outside the core. In the case of a simple inductor, this does not represent an energy loss term per se, but merely makes it more difficult to compute accurately the inductance from the geometry. In the case of a transformer, it looks like a small series inductance, still not lossy, in series with the transformer. If the leakage flux couples to something lossy, like a steel fixing bracket, then that creates an energy loss by transformer action when the current and flux changes.

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