# current induced on an inductor modifying inducing magnetic field. Wouldn't that cause an infinite oscillating feedback?

Imagine a simple circuit with an inductor and resistor in series.
Now pass thru a varying flux thru the inductor, a phi.

The vary flux induces voltage on the inductor to oppose the flux causing a current to flow in the circuit. That current generates its own flux phi_i. phi_i would counter phi, causing total flux thru the inductor to lessen. The voltage induced on the inductor is now less, current in the circuit is less, phi_i would lessen, so the total flux thru the inductor, phi - phi_i now rebounded a bit. Which will then cause phi_i to increase and start the whole chain again.

current in the coil is affected by the total flux, and total flux is affected by the current in the coil, we have a "chicken-and-egg" scenario here.

I admit this is a very crude way of thinking, as the voltage induced on the inductor doesn't depend on the magnitude of the phi but the change rate. However, the current and voltage aren't induced instantaneously either, so the real dynamics of the total flux is quite complex to think thru. I think.

• Did not attract any attention when first posted. However I welcome any answers/comments anytime. I visit the site frequently – ugn May 4 at 15:09

You are getting tangled up in a verbal description of what is actually an easily analyzable problem. One must use mathematics to analyze it.

The result is, if the external flux changes only once at the beginning, there is no infinite oscillation because the resistor dissipates energy into heat. If the circuit had only inductor and capacitor instead of resistor, it would oscillate much longer, but still not indefinitely, because it would lose energy by other means - by radiation.

If the external flux keeps changing, the current in the circuit will keep changing too. The external flux change acts as a driving force for the circuit and it supplies energy to it.

For a circuit of inductor in series with resistor, while the inductor is driven by the external flux change $$\frac{d\Phi_0}{dt}$$ ($$\Phi_0$$ is total effective flux for the coil at hand, for a different coil same magnetic field would have different flux), the equation of motion for electric current $$I$$ is

$$RI + L\frac{dI}{dt} + \frac{d\Phi_0}{dt} = 0.$$

Since it is first order differential equation, there can be no oscillation in the solution for current $$I$$, unless the oscillation is put in via $$\Phi_0$$.

• Thank you. I probably shouldn't have used terms of "oscillation" and "feedback". My question is regarding thephi0 in your equation. that effective flux is the result of inputFlux + current, but current itself is also the result of effective flux, It is a chicken and egg problem, does current and effect flux affect/feedback to each other to infinity or is it just a one time thing? – ugn May 4 at 22:43
• (Note, the input flux is constant, a steady sinusoidal flux for example, the input flux is NOT the total flux) – ugn May 4 at 22:49
• Rate of change of external effective flux through the coil is $d\Phi_0/dt$. Rate of change of total effective flux through the coil is $LdI/dt + d\Phi_0/dt$. Both contribute in the same way in the equation. Both external and internal induced electric field influence the current. – Ján Lalinský May 5 at 14:03