# Should the magnetic field outside a conductor be considered?

I've simulated a circular disc where a magnetic field is moving out of the page. The arrows in the picture represents the direction of its current density.

I'm wondering, will the induced current produces another external magnetic field near the edge of the disc? If yes, will that external magnetic field influences each other when the current changes? Should that field be concerned or can be negligible and why? This is because most sources I've read only concerned about the internal field.

• So, to be clear, you simulated what happens to a conductive disk when a magnetic field orthogonal to it is increasing or descreasing, right? In that case the current density goes like the induced electric field. If that field will concatenate an appreciable variable magnetic field depends on how fast things are changing. That's the difference between magnetoquasistatic and electrodynamics. Commented Jan 30, 2021 at 20:46
• There is an important information you need to supply: is the conductor perfect? Because I can see two ways this system can behave, both in a mqs context. Simplify the problem to a ring of conductive material. Now if the ring is resistive the current is limited by resistance and the B field can be influent. But of the ring has zero resistance, the current will rise so fast that the magnetic field it creates will oppose the original magnetic field effect; in this case the current is limited by the self-inductance of the ring. Commented Jan 30, 2021 at 22:27

I'm wondering, will the induced current produces another external magnetic field near the edge of the disc?

Yes it will and it's not an induced current it's an eddy current caused by an induced voltage in the conductive disc that circulates the eddy currents. Faraday is clear about this; voltage is induced and that's why we have faraday's law of induction related to voltages and not currents.

If yes, will that external magnetic field influences each other when the current changes?

If you mean will it influence the alternating magnetic field that created the eddy currents then yes it will. Due to Lenz's law it will seek to reduce that originating field within the disc: -

But, the eddy current field will enhance the originating field outside the disc.

Should that field be concerned or can be negligible and why?

I don't understand that question; probably a bad choice of words but, taking a guess, it might be negligible but that's truly down to what a person decides is or isn't negligible.

• I paraphrased my last question: Can we ignore the influence to the current which is caused by the external magnetic field? Is the influence significant or is it too small that it can be negligible? Commented Jan 31, 2021 at 7:37
• @Theta sorry, I'm still not understanding that last question. Commented Jan 31, 2021 at 9:55