Please explain - total electic field Ec + En within the coils must be zero

[bksree]

Please explain -- total electic field Ec + En within the coils must be zero

Hi
This is from the text University Physics.
In pg. 1035, chap 10, in order to justify the use of Kirchoff's rule to analyze circuits containing inductors it is written :
Let's assume we are dealing with an inductor whose coils have negligible resistance. Then a negligibly small electric field is required to make charge move through the coils, so the total electic field Ec + En within the coils must be zero, even though neither field is individually zero.

The doubt is : Why should En + Ec be zero ?


TIA
sree

 

[Gordianus]

I don't know what En and Ec mean, but I strongly recommend reading Walter Lewin's lecture on induced fem. He addresses the question why the electric field inside a good conductor should be very small.

 

[bksree]

Ec - conservative electric field (Couloumb's law)
En - non conservative electric field (induced field due to change in flux)

 

[Gordianus]

The voltage drop across an inductor, L dI/dt can be large. However, if you try to equal this figure to the integral of the electric along the coil wire you find a small number because, for any finite current, the field inside a good conductor must be very small.
How do you reconcile both points of view?
Walter Lewin shows how L dI/dt equals the integral of the electric field outside the coil.
I strongly suggest that you watch Lewin's lectures; they're free.

 

[pmacias]

Hello Sree,

Thank you for your question. The reason that the total electric field Ec + En within the coils must be zero is because of the nature of inductors. An inductor works by creating a magnetic field when current passes through it. This magnetic field, in turn, induces an opposing electric field within the coils. This opposing electric field is what causes the inductor to resist changes in current.

Now, in the case of an ideal inductor with negligible resistance, the flow of current is not hindered by the coils themselves. This means that the electric field within the coils must be negligible as well. If there were a significant electric field within the coils, it would require energy to maintain it, which would result in a loss of energy and a non-ideal inductor.

Therefore, in order for an inductor to function as it should, the total electric field within the coils must be zero. This ensures that there is no loss of energy and the inductor can effectively create a magnetic field to oppose changes in current. This is why we can use Kirchhoff's rule to analyze circuits containing inductors, as the total electric field within the coils is negligible and can be ignored in our calculations.

I hope this helps to clarify the concept. Please let me know if you have any further questions.

Best,