# Magnetic field and electric field induce one another forever [duplicate]

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?

• possible duplicate of Induced magnetic field produces electric field and vice versa forever! – Rob Jeffries Apr 4 '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 4 '15 at 11:01
• 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. – Rob Jeffries Apr 4 '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 4 '15 at 11:12
• 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 4 '15 at 12:41