Isn't there a loop in maxwell's equations?

Question

I am curious about the following case:

Consider the electrical field in a particular point just changed for some reason. Then by the maxwell's equations, there will be magnetic field generated circularly around the plane of change (which I should be symmetrical, I assume).

However this newly generated magnetic field will cause the points around the orign of change to have varying magnetic field, then they will also produce electrical field by the maxwells laws.

And this recursive loop seems to continue until infinity in a converging manner. I was wondering does it ever come to steady state, do those generated series of electrical and magnetic fields converge into a function as in taylor series? Or do maxwells equation already takes that into account and just states the resulting field distribution considering this recursive loop?

I really hope I expressed it well enough, please let me know if you need some clarification.

This has been asked a number of times recently. I'll try to dig up one of the more recent incarnations of the question. — Kyle Kanos, May 09 '15 at 20:43
Canabrigian: Are you referring to generation of electromagnetic waves? — Gonenc, May 09 '15 at 21:28
Sorry if that is a repost however I couldn't find anything specifically asks the same thing. At least the ones I come up with were referring to the electromagnetic radiation, but I don't think this question refers to that. (But well, I am not sure since I ask the question) — ozgeneral, May 09 '15 at 23:28
Is this called as electromagnetic waves? And are electromagnetic waves different than electromagnetic radiation? Because I am sure this is not about electromagnetic radiation since it needs acceleration to exist — ozgeneral, May 09 '15 at 23:30
possible duplicate of Induced magnetic field produces electric field and vice versa forever! — Kyle Kanos, May 10 '15 at 01:53
See also http://physics.stackexchange.com/q/181277/ (likely more informative than the proposed duplicate, but the dupe is much closer aligned in question than this link is). — Kyle Kanos, May 10 '15 at 01:54

Isn't there a loop in maxwell's equations?

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