Electric/Magnetic vicious cycle

[Dorian Black]

Apologies for the melodramatic title.

In studying AC current distribution in cables (skin effect), one can view the AC current as producing a time varying magnetic field in phase with the current itself (Ampere's Law). This in turn creates an electromotive force 90 out of phase with the current (Farady's), eventually bringing about an induced current in the wire itself. You add these up and arrive at the current distribution. My question: Can one look at the induced current (obtained through Farady's Law), and then calculate the current it induces itself since it is also time varying and creates an alternating magnetic field. Thus we arrive at an induced current created by another induced current, which can also be subjected to the same analysis. Would this 'infinite series' eventually bring about the same result, or is it faulty from the outset? And if so, why exactly? Many thanks.

 

[Delta2]

What you refer to is an iterative method for solving maxwell's equations. Though i sense this method isn't mathematically correct and will not give exact solution (even if one manages to calculate the sum of infinitely many induced currents) still you can get good approximate solutions by this method. What you ll want to do is just to stop after the Nth iteration for some N and just ignore the effect of the Nth induced current (so we ignore the Nth+1 induced currents and all the rest). The bigger the N you chose to stop the more exact the solution will be.