Why does skin depth approach zero at DC if it decreases with frequency?

[goodphy]

Hello.

The skin depth is nothing but measure of penetration depth of EM Wave when it is incident on the conductor. It is well known that the skin depth is decreased when the EM wave frequency increases. But thinking about DC field. We know that when DC is applied to metal (metal is installed between two electrodes) field inside the metal should be zero as charges are distributed according to the external field and the result is not external field and the field due to space charge are canceled out each other. Thus maybe we can say that skin depth of DC is zero as field can not existed inside the conductor right? This is contrary to typical knowledge of skin depth that it is decreased as frequency raises.

And one more question: why skin depth decreases as incident frequency increases in AC? I imagine that in higher frequency, electrons have to respond faster than case of lower frequency thus they feels harder to shield field.

 

[Delta2]

Hello.

In the case of DC current the E-field inside the conductor is NOT zero and it penetrates fully the conductor. The E-field is necessary to keep the DC-current alive , otherwise the current will decay to zero fast, because there will be no force from the electric field to give energy to the free electrons and the free electrons will soon lose all their kinetic energy due to impacts with the atoms of the conductor. So we can say that in case of DC current the skin depth is maximum.

Skin depth decreases with higher frequency cause that's what we get from the study of this phenomenon using maxwell's equations. I think a more intuitive explanation would be that the induction process in the conductor becomes stronger at higher frequencies and the induction process is always such as to oppose the changes in the current.

 

[tech99]

Hello.

In the case of DC current the E-field inside the conductor is NOT zero and it penetrates fully the conductor. The E-field is necessary to keep the DC-current alive , otherwise the current will decay to zero fast, because there will be no force from the electric field to give energy to the free electrons and the free electrons will soon lose all their kinetic energy due to impacts with the atoms of the conductor. So we can say that in case of DC current the skin depth is maximum.

Skin depth decreases with higher frequency cause that's what we get from the study of this phenomenon using maxwell's equations. I think a more intuitive explanation would be that the induction process in the conductor becomes stronger at higher frequencies and the induction process is always such as to oppose the changes in the current.

It is sometimes said that the current at the centre of a conductor is circled by more magnetic field lines than that at the surface. This gives it higher inductance, which has no effect at DC, but for high frequencies makes it harder for current to flow in the centre. I am not sure how this fits with the EM wave explanation.