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I'm reading the document "Eddy Current Losses in Transformer Windings and Circuit Wiring" by Lloyd H. Dixon, Jr about proximity effect in transformer and more generally. I have a misunderstanding point. Here it is:

Fig. 5 - Circuit Wiring - Flat Parallel Strip from "Eddy Current Losses in Transformer Windings and Circuit Wiring" by Lloyd H. Dixon, Jr

Fig. 5 - Circuit Wiring - Flat Parallel Strip
"Eddy Current Losses in Transformer Windings and Circuit Wiring" by Lloyd H. Dixon, Jr

As the current direction in the two strips is opposed, the magnetic field is very high between the two strips as each magnetic field of each strip adds each other. Nevertheless, according to Faraday's Law and Lenz's Law, I do not understand why the eddy current are not maximum at the place where the magnetic fields is maximum. Hence if the eddy current is maximum at this place, the eddy current being opposed to the current flowing into the conductor, the current should be lower at the place where the magnetic field is maximum?

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The eddy current is flowing such that it enhances the magnetic field produced by the main current. It is in contradiction with the Lenz's Law and physically this is not possible because I do not understand where the equilibrium is reached. Please bring me to the light !

Lenz's Law = "the direction of the current induced in a conductor by a changing magnetic field is such that the magnetic field created by the induced current opposes the initial changing magnetic field."

Thank you very much.

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I do not understand why the eddy current are not maximum at the place where the magnetic fields is maximum

They are, but....

An eddy current will circulate current in each parallel strip therefore, an eddy current neither adds-to nor diminishes the main current flow in the plate. That main current flow still occupies that part of the plate that has the least inductance and actually, the eddy currents will diminish that inductance a little.

Hence if the eddy current is maximum at this place, the eddy current being opposed to the current flowing into the conductor, the current should be lower at the place where the magnetic field is maximum

No, it neither detracts nor enhances the main current because it is an eddy and eddies circulate.

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  • \$\begingroup\$ Thank you for your reply. "The main current flow will occupies the part of the plate that has the least inductance, the eddy current will diminish that inductance a little" You mean that eddy currents diminish the magnetic field produce by the main current #Lenz's Law. ? If the magnetic field is lower then the total current is lower ? I m confused ... \$\endgroup\$ – Jess Mar 21 '20 at 15:42
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    \$\begingroup\$ Yes, the eddy currents act like a partially shorted turn on the secondary of a transformer and, when that happens, the inductance of the primary appears to reduce. Imagine a coil of wire excited with an AC voltage; a certain current will flow due to the coil's inductance but if you bring that coil of wire close to a conducting object, the inductance will fall as eddy currents flow in the conducting object. This means that the magnetic field IS reduced and current is greater. \$\endgroup\$ – Andy aka Mar 21 '20 at 15:53
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    \$\begingroup\$ That's fine, I realized that it's a lot to take in. An alternative approach is to consider a transformer and think about the phase angles going from primary voltage (0 deg) to magnetization current (-90) to magnetization flux (also -90) to induced secondary voltage aka the voltage that creates eddy currents. That induced voltage is back to 0 degrees and it creates an eddy current at close to 0 degrees due to material resistance. That eddy current is at 90 degrees to the mag current and neither helps nor hinders that current..... But.... \$\endgroup\$ – Andy aka Mar 22 '20 at 9:26
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    \$\begingroup\$ .... In the real world the eddy current is not quite 0 degrees but slightly in phase with the mag current hence there is a tendency to take more current which, appears as a reduction in inductance. Magnetism can be really hard to get your head around sometimes. \$\endgroup\$ – Andy aka Mar 22 '20 at 9:27
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    \$\begingroup\$ Please add the link to the physics forum @Jess \$\endgroup\$ – Andy aka Mar 22 '20 at 15:23

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