# How is the rate of current change in an inductor present in a circuit maintained / decreased?

Considering an ideal circuit of DC voltage source and an inductor connected together with a switch in between them. When the switch is closed at t=0 the current starts increasing which causes induced EMF which in turn results in non-conservative electric field, in order to maintain 0 electric field inside a conductor(ideal) electric charges accumulate to cancel the non-conservative field, due to which voltage develops across the inductor(as it is defined for static fields) but the net electric field is zero inside the ideal inductor, from the equation of EMF= -L(di/dt), I understand that current should change for the EMF to exist but from the argument I just mentioned above I feel that there is no electric field inside and hence the current should remain constant, which causes the induced EMF to become zero(as there is no change in current now) and also the electric field due to accumulated charges on the surface of inductor also vanishes, so now how is the rate of current change maintained? What causes it to be maintained that is what causes it to exist? Please give an intuitive explanation of how this happening.

I have read that induced EMF is causing the rate of current to decrease(in general) but how according to the argument I mentioned above?

And what does the rate of change of current mean? Is it the increase in velocity of charges? Or increase in number of charges?

I know there is some flaw in my explanation, I am surely missing out something so please help me out.

## 1 Answer

there is no electric field inside and hence the current should remain constant,

In case of ideal inductor and ideal DC source, the increase of current does not require presence of substantial net macroscopic electric field in the wire. There is strong Coulomb field of the battery and surface charges but inside the wires this field is almost cancelled out by the induced electric field due to the charge carriers in the inductor.

Of course, on the microscopic level of description, there has to be some small non-zero force that accelerates the current carriers in the direction of the current to make them move faster. Thus the Coulomb field of the battery and surface charges is a little greater than the induced electric field, so some net work is done on the charge carriers in increasing their kinetic energy. But this accelerating force is, on the macroscopic scale, negligible, because charge carriers are extremely light, and there is (by assumption) no ohmic resistance.

When you calculate kinetic energy of mobile electrons in an inductor, it is many orders smaller than magnetic energy stored in the inductor. So net force (sum of the Coulomb forces and forces of the induced electric field) needed to accelerate them is negligible compared to the net Coulomb force, and thus net electric field is pronounced effectively zero.

• can I say gauss' law is applicable to macroscopic field from your answer? – Trilok Girish Kamagond Jul 7 '19 at 17:25
• Macroscopic electric field obeys Gauss law, yes, but why are you asking? My answer was not about that. – Ján Lalinský Jul 7 '19 at 21:37
• Since Gauss' law says that net charge is zero inside a conductor(no electric field) so I was asking basically that Gauss's is only applicable to macroscopic fields? Since in the answer you also tell about microscopic fields existing. – Trilok Girish Kamagond Jul 8 '19 at 7:21