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A changing electric field produces magnetic field and vice versa. Does that mean that this process will carry on forever? Think of a circuit with a capacitor. The magnetic field due to the current at a point on the wire (by the Ampere-Maxwell law). But the current was changing with time, so it also meant that the magnetic field changed. And a changing magnetic field produces an electric field, so we have to go back again from the start by Ampere's law. It seems that this will go on forever. What is the final magnetic and electric field that I have to calculate?

ACuriousMind
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TheQuantumMan
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    possible duplicate of Induced magnetic field produces electric field and vice versa forever! – ProfRob Apr 04 '15 at 10:59
  • i wrote both of them.But that did not get more than one answers because i made the question look like a specific example.This is more general – TheQuantumMan Apr 04 '15 at 11:01
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    Why is this any different to saying - the velocity of the mass of a spring depends upon its displacement; but the displacement changes with time, so how do I find the velocity. The answer is you have to solve the coupled differential equations, with boundary conditions. In the case you mention (capacitor in a dc circuit), obviously the current and B-field in the wire all tend to zero at large t, as does the rate of change of E-field. – ProfRob Apr 04 '15 at 11:08
  • Yeah,but i do not know how to derive this.Maybe this is why it initially seems to be going on forever – TheQuantumMan Apr 04 '15 at 11:12
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    Landos, I don't recommend thinking in terms like "the changing E field begat a changing B field which then begat a changing E field" unless you're thinking of some kind of an iterative solution. Rather, think more in terms of "if the B field is changing with time, there is an associated (non-conservative) E field" and these must, at all times, satisfy Maxwell's equations. – Alfred Centauri Apr 04 '15 at 12:41
  • But isn't this what is really happening?Why should we ignore it? – TheQuantumMan Apr 04 '15 at 12:47
  • Landos, you already have my recommendation. – Alfred Centauri Apr 04 '15 at 15:26
  • Here is Alred's comment rephrased, in case it helps: The magnetic field and electric field are "one and the same thing", the point being that I can derive the magnetic field from the (changing) electric field and vice versa. So at any point in time for your system (circuit with changing current), the electromagnetic field is $(B(t),E(t))$ and they satisfy the relations that you describe (i.e. the Maxwell equations). – Chris Gerig Apr 04 '15 at 20:40
  • So,you both say that the process does not go on forever,but only once.And that one time has to satisfy both of Maxwell's equations,so i must calculate once the magnetic field due to the current and then calculate once the changing electric field due to that changing magnetic field.Right? – TheQuantumMan Apr 05 '15 at 09:42

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The idea in the comments above is a good one. The reason you don't need to worry about the order is that you're looking for an equilibrium solution. In terms of going on forever, it's broadly true. I mean electro magnetic radiation is exactly the kind of effect you're talking about. In a circuit there is normally a dissipative term, but in a steady state with a power supply you just need to solve the equations simultaneously

Dr Xorile
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  • But i am not refering to a steady-state.I am talking about a time changing current.So,why doesn't this go on forever? – TheQuantumMan Apr 04 '15 at 19:54
  • It does keep oscillating. That's the steady state you're solving for. It normally has a i" ~ -i, type equation which leads to an oscillating solution – Dr Xorile Apr 04 '15 at 20:11
  • So,if i understood correctly,the process does not go on forever,but only once.And that one time has to satisfy both of Maxwell's equations,so i must calculate once the magnetic field due to the current and then calculate once the changing electric field due to that changing magnetic field.And IF those solutions give me an equation which describe an oscillation,then it is oscillating.Otherwise,they just dissipate.Right? – TheQuantumMan Apr 05 '15 at 09:44