# Electric shielding skin depth

I read that lower the frequency,the deeper is the skin depth in conductor.If we are using piece of thin conductor,like aluminum foil for example to shield something from electric fields,it would shield less and less the longer the wavelenght is becose skin depth keeps getting longer and since the thickness of the shield is fixed,it will block less and less energy.

My question is this,why is it possible to shield against electrostatic field if DC electrostatic field have infinite skin depth?

How can Faraday cage work? Since the shielding becomes progressively weaker the lower we go in frequency,and frequency can be infinitely low but somehow,DC electric field can be blocked,they dont possess infinite penetration,it logicaly suggest that for some reason,at some frequency,skin depth stops increasing.But that sounds like nonsense to me,I cant think of single reason why it would act like that.

What we call DC is reality extremly low frequency,true DC would need to last for infinte duration which doesnt happen in reality.When you charge HV probe for 100 seconds to test the shield its truly 0.01 Hz frequency,so it should have huge penetrating power,yet relatively thin shield can block it,why?

• @safesphere Electric and magnetic fields are not physically independent quantities. – my2cts Aug 11 '18 at 10:10
• The zero frequency case here is that of a stationary current. Such a current will be evenly distributed through the volume. – my2cts Aug 11 '18 at 10:19
• @my2cts The static fields are independent, but I see your point though that in a wave they are not, because they belong to the same photons. – safesphere Aug 11 '18 at 16:08
• "What we call DC is reality extremly low frequency" - No, this is not true. A wave of any frequency travels with the speed of light, but the static field doesn't. If you move a static field, you accelerate it. This creates a pulse of a wave that travels out with the speed of light. Once you stop accelerating, the field becomes static again (in its frame of reference). – safesphere Aug 11 '18 at 16:18
• @safesphere. What is then difference between turning "static" electric field on and off every 100 seconds and 0.01 Hz square wave? – wav scientist Aug 11 '18 at 17:05

From the context, I assume that by a DC field, you really mean a static electric field.

When you place a Faraday cage in a static field, the field will initially penetrate the cage, but, after a short period of time, the field inside the cage will become zero due to the redistribution of electrons in the cage.

When you place a Faraday cage in a slow changing (or low frequency) electric field, the field will penetrate the cage and the electrons will redistribute themselves in an attempt to cancel the field inside the cage, but, since the field keeps changing, a full cancellation cannot be achieved.

At lower frequencies though the cancellation will be more complete than at higher frequencies. This is because, the cancelling field, produced by redistributed electrons, will be able to track the applied field much closer (smaller phase delay) and, therefore, the difference between them (i.e, the residual field inside the cage), at any given point in time, will be smaller.

It is easy to see that, if the external field changes really slowly (in the limit), the field inside the cage would be so small that we could consider it it to be zero.

So, as far as the effectiveness of the Faraday cage is concerned, there is no sharp transition between slow changing (low frequency) fields and a static field.

• Interesting,so at high frequencies,as we decrease the frequency the penetration gets bigger becose skin depth gets deeper,but at some point in low frequency range,as we go even lower in frequency the penetration stops increasing and actually starts decreasing.Is that statement correct? What kind of frequency is that critical point where it starts to reverse? Does this reversal frequency vary between different conductors? – wav scientist Aug 13 '18 at 9:57
• @wavscientist I have not done any simulations or measurements, but I was thinking of the Faraday cage as a low pass filter, in which case, as long as the frequency of the field is lower than the cut-off frequency, the output (cancelling field) could follow the input (applied field) pretty closely. Higher resistivity of cage material should reduce the cut-off frequency, i.e., make the cage less effective. – V.F. Aug 13 '18 at 11:21
• What do you mean by cut off frequency? I am EE noob but it reminds me of linear regulator with feedback,as long as the frequency is low,the feedback is fast enough to cancel any voltage variations but if they are too fast,the AC voltage canceling capability drops becose it cant keep up.Now the important part : isnt it more accurate to desribe it as bandpass filter? You didnt mention the essential fact that the penetration increases with lowering of frequency,I believe what you say that at some point things reverse and lower frequency = less penetration,but that means its bandpass filter curve. – wav scientist Aug 13 '18 at 11:57
• @wavscientist It depends on what we choose as an output. If the output is the resulting field inside the cage, it as a bandpass filter. If the output is the cancelling field inside the cage, it is more of a low pass filter. – V.F. Aug 13 '18 at 12:34
• So there are two factors that determine the blocking,one is the field cancelling,and other is increasing resistive losses due to decreasing skin depth.Even though from the point of view of impedance,resistance is non-reactive frequency flat thing,due to the changing skin depth,the resistance changes too so its not a flat & frequency blind anymore.That means from the perspective incoming field in terms of penetration,skin depth acts as low pass filter,blocking more higher frequencies,and your field cancelation effect as high pass filter,blocking more lower frequencies,together its bandpass. – wav scientist Aug 13 '18 at 13:47

The concept of skin depth is developed in Jackson's Classical Electrodynamics, in chapter 5, section 5.18A of the third edition. If you work through the math, you will see that the approximations fail for the DC case.

OTOH, it is well known from experimental science that longer wavelengths penetrate further. And yes, Faraday cages work at all frequencies, if they are built correctly - they can have holes if the wavelength is longer than the hole size (e.g., microwave screens).

So you need to understand the physical basis for an approximation, or any formula, in order to know its limits.

The confusion is coming from the fact that the electric field inside an isolated conductor is zero. This is true in the static limit when all charges have had time to settle.

For conduction the limit to zero frequency we should consider a conductor that is part of a circuit so that a stationary current can run. Assuming a finite resistance $\sigma$ a static external electric field will pervade the conductor and a current density $\vec j =\sigma \vec E$ will be present. This may be uniform depending on the geometry and there will be no skin effect.