# Floating electrostatic shield

Hello,

I am trying to fully wrap my head around signal shielding so as to take it from the trial-and-error domain to the theoretical design domain. The problem is that I am stuck on one of the very basic and fundamental principles of shielding - the floating conductor as an electrostatic shield.

I am reading a textbook "Grounding and Shielding Techniques in Instrumentation" by Ralph Morrison. According to Morrison, any fully-closed conducting surface is enough to keep external shields out and internal fields in. The reason a shield should be tied to reference has to do with feedback gain elements. Colleagues in my field always say that a shield should be grounded so that shield currents "have a place to drain to," but I don't believe this is correct according to Morrison's explanation.

Lets say we have a conductor (small sphere or point charge) with excess + charge surrounded by a floating conductor shell with no excess charge. How is there no field outside of the shell? Two theories tell me that there must be a field outside.

1: Gauss's law - The total charge inside the entire volume is not zero due to the excess charge of the inner conductor. Then, the surface integral cannot be zero, meaning that the electric field is emanating away from the system. A time-varying field in the inner conductor would still generate an EM wave outside of the system.

2: Circuit theory - (capacitors shown)

------||------||---------
a............b............c

if 'a' is the inner conductor, it will have a capacitance to the outer conductor, 'b', and that outer conductor will have a capacitance to another conductor, 'c', such as ground. Just because we added a capacitor in series doesn't nullify the capacitance between 'a' and 'c' at all.

Am I misunderstanding Morrison? I would think that a grounded or voltage-controlled shield would be mandatory, because the charges in the outer conductor would migrate into/out of ground or voltage controller, establish charges equal in magnitude and opposite in polarity on the outer conductor, and Gauss's law would yield a surface integral of 0. Then, external fields remain external, internal fields remain internal.

What am I missing about the floating/unreferenced shield? How is it effective? Does it just slightly reduce capacitance?

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Born2bwire
Gold Member
Let's just take a charge Q and place it at the origin and then encase it in a spherical conducting shell. Outside of the shell there will be a field just as if there was no conducting shell at all. We know this because we can use Gauss' Law to find the field. The enclosed charge did not change by adding the shield because the shield is neutrally charged. However, on the inner surface of the shield there is a net induced charge of -Q and on the outer surface is a net charge of Q. We know this because the net field inside the conductor must be zero and thus we know that the flux over a Gaussian surface inside the conductor must be zero and thus the net charge is zero.

But, if we connect the outer surface to ground, then when the inner surface gets an induced charge of -Q, the outer surface remains neutral because all the oppositely charged particles that would normally make up the Q charge on the outer surface get sinked into the ground. Thus now the net charge outside of the shield is zero.

Another way of thinking of it is that if we start with a grounded shield, its potential will always remain at 0 V. If we introduce a net charge inside of the shield's volume, then the charge will simply draw out opposite charges from the ground as it needs them. It will keep drawing out opposite charges until there is no net field left to carry the charges from the ground to the inner surface.

Now for electromagnetic waves, a perfectly electrically conducting sphere will block all incoming and outgoing waves. This is regardless of the grounding of the shield. So the grounding of the shield helps it with static charge buildups. Although it wouldn't surprise me if grounding a Faraday cage does improve performance due to real world limitations.

Hello,
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1: Gauss's law - The total charge inside the entire volume is not zero due to the excess charge of the inner conductor. Then, the surface integral cannot be zero, meaning that the electric field is emanating away from the system. A time-varying field in the inner conductor would still generate an EM wave outside of the system.

2: Circuit theory - (capacitors shown)

------||------||---------
a............b............c

if 'a' is the inner conductor, it will have a capacitance to the outer conductor, 'b', and that outer conductor will have a capacitance to another conductor, 'c', such as ground. Just because we added a capacitor in series doesn't nullify the capacitance between 'a' and 'c' at all.
...

1. Gauss law tells you only the total charge inside the shield. If that does not vary (conservation of charge) you cannot tell a non-stationary source inside the shield will generate a non-stationary field outside. In addition an ideal conductor is an ideal reflector for electromagnetic waves.

2. For an ideal hollow conductor you cannot create a potential difference between interior and exterior surface so its capacitance is infinite.

In real life ideal conductors do not exist and stuff will get through: very high frequencies, magnetic fields, etc so grounding sounds like a good idea.

Hello,

I am trying to fully wrap my head around signal shielding so as to take it from the trial-and-error domain to the theoretical design domain. The problem is that I am stuck on one of the very basic and fundamental principles of shielding - the floating conductor as an electrostatic shield.

I am reading a textbook "Grounding and Shielding Techniques in Instrumentation" by Ralph Morrison. According to Morrison, any fully-closed conducting surface is enough to keep external shields out and internal fields in. The reason a shield should be tied to reference has to do with feedback gain elementsNo idea what you meant.. Colleagues in my field always say that a shield should be grounded so that shield currents "have a place to drain to," but I don't believe this is correct according to Morrison's explanation.

Lets say we have a conductor (small sphere or point charge) with excess + charge surrounded by a floating conductor shell with no excess charge. How is there no field outside of the shell? If the shell is floating, you will see the field outside the shell as if there is no shell. Read the examples in most EM books on a charge surrounded by a conducting hollow sphere.Two theories tell me that there must be a field outside.

1: Gauss's law - The total charge inside the entire volume is not zero due to the excess charge of the inner conductor. Then, the surface integral cannot be zero, meaning that the electric field is emanating away from the system. A time-varying field in the inner conductor would still generate an EM wave outside of the system.

2: Circuit theory - (capacitors shown)

------||------||---------
a............b............c

if 'a' is the inner conductor, it will have a capacitance to the outer conductor, 'b', and that outer conductor will have a capacitance to another conductor, 'c', such as ground. Just because we added a capacitor in series doesn't nullify the capacitance between 'a' and 'c' at all.

Am I misunderstanding Morrison? I would think that a grounded or voltage-controlled shield would be mandatory, because the charges in the outer conductor would migrate into/out of ground or voltage controller, establish charges equal in magnitude and opposite in polarity on the outer conductor, and Gauss's law would yield a surface integral of 0. Then, external fields remain external, internal fields remain internal.

What am I missing about the floating/unreferenced shield? How is it effective? Does it just slightly reduce capacitance?

You need to ground the shield to drain the charge induced on the outside of the shield. People usually don't worry too much about static field, it is the varying EM field that is troublesome. Not only you have to ground the shield, you have to have grounding on multiple points with spacing less the 1/10 of the wavelength of the highest frequency component.

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Born2bwire
Gold Member
You need to ground the shield to drain the charge induced on the outside of the shield. People usually don't worry too much about static field, it is the varying EM field that is troublesome. Not only you have to ground the shield, you have to have grounding on multiple points with spacing less the 1/10 of the wavelength of the highest frequency component.
You do not need to ground the shield let alone ground it at regular distances like you describe (given that cell phones have wavelengths on the order of 10 cm our Faraday cage would look rather ridiculous having connection points for a star ground at 1 cm intervals). However, we do not necessarily need a solid sheet of conductor for our shield. We can use a wire grid and the size of the air gaps in the wires need to be something on the order of a fraction of a wavelength. Typically at most a quarter of a wavelength but it depends on the thickness of the grid and how much attenuation you need. Perhaps that is the configuration that you are thinking of.

You do not need to ground the shield let alone ground it at regular distances like you describe (given that cell phones have wavelengths on the order of 10 cm our Faraday cage would look rather ridiculous having connection points for a star ground at 1 cm intervals). However, we do not necessarily need a solid sheet of conductor for our shield. We can use a wire grid and the size of the air gaps in the wires need to be something on the order of a fraction of a wavelength. Typically at most a quarter of a wavelength but it depends on the thickness of the grid and how much attenuation you need. Perhaps that is the configuration that you are thinking of.
The op talk about his co worker talk about grounding of the shield, that is the reason I am concentrate on the pratical circuits. You do need to ground the shield to block the electric field or else it would be invisible because the charge will just induce outside and the electric field will emit out as if the shield is not there.

If you are work in micro wave region, if you have bigger gap between grounding the shield will not act as perfect ground. That is the whole thing about quarterwave stuff that a short circuit become a true open circuit. grounding between quater wave length is not enough, standard is pretty much 1/10 wave length.

I have many years working in signal integrity, pcb design in term of EM shielding. Problem with just study the theoretical EM is people only worry about the signal but in reality it is the ground return that really give people problem. It is the return path......the IMAGE current path that is the real killer in mix signal high speed enviroment. I was in charge for large equipments to pass CE ( similiar to UL) on EM emission for years. That is the reason we use RF gasket to seal the enclosure. Or else we have to have screws in short spacing to screw the lid tight to provide the grounding.

In fact in my years of signal integrity and high speed mix signal design, and I constantly work in 10K to 15KV enviroment. I never once use a cage seal yet!!! Never have to resort to that, I deal with signals in micro volts in high speed digital signal enviroment and never once have to resort to that yet. Emission from a bad ground plane that break the immage return current cause more damage than anything else in my experience.

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Born2bwire
Gold Member
You do need to ground the shield to block the electric field or else it would be invisible because the charge will just induce outside and the electric field will emit out as if the shield is not there.

If you are work in micro wave region, if you have bigger gap between grounding the shield will not act as perfect ground. That is the whole thing about quarterwave stuff that a short circuit become a true open circuit. grounding between quater wave length is not enough, standard is pretty much 1/10 wave length.

I have many years working in signal integrity, pcb design in term of EM shielding. Problem with just study the theoretical EM is people only worry about the signal but in reality it is the ground return that really give people problem. It is the return path......the IMAGE current path that is the real killer in mix signal high speed enviroment. I was in charge for large equipments to pass CE ( similiar to UL) on EM emission for years. That is the reason we use RF gasket to seal the enclosure. Or else we have to have screws in short spacing to screw the lid tight to provide the grounding.

In fact in my years of signal integrity and high speed mix signal design, and I constantly work in 10K to 15KV enviroment. I never once use a cage seal yet!!! Never have to resort to that, I deal with signals in micro volts in high speed digital signal enviroment and never once have to resort to that yet. Emission from a bad ground plane that break the immage return current cause more damage than anything else in my experience. And yes this is real life experience, you cannot just use the theory alone.

The op talk about his co worker talk about grounding of the shield, that is the reason I am concentrate on the pratical circuits. In fact, there is no "floating charge" in the practical world. We do TOF mass spectrometer and we generate electric field for deflection using high voltage driving the deflector plates, nothing floating about it in real life.
Perhaps you could explain by what you mean grounding at 1/10 wavelength intervals. Like I said, that would make our Faraday cages and shields patently ridiculous to have grounding points like that. For a good shield you should probably ground it at multiple points but in no way do you need to ground it like you are talking about. Heck, look at your microwave, there are no ground points in the window screen, it's just a sheet of conductor with holes though there could be ground connections at some point along the periphery though I have never disassembled one to the point to find out.

If you look at any RF designed enclosure, you'll see. You'll see they have screw every inches spacing to ensure the lid is connect tight to the box. Also some use RF gasket to get even tighter seal.

We use quarter wave Tx line to guarentee an open circuit by using a micro strip quarter wave long and grounded on one side and at the desired frequency, the other end guarentee an open circuit. This is commonly used as a band pass filter that short out all other frequences and only provide an open circuit to let the desired frequency to pass through.

Let's say the shield has two points grounding and half a wave length apart. Right at the mid point it is quarter wave from either grounding point. Around that area, the shield become a floating shield and EM just goes right through. It behaves like a big gap on the shield.

I have both kind of EM books 1)EM books for electrical engineering and 2) both Griffiths and JD Jackson. Only the the books for EE like "Fields and Waves Electromagnetics" by David K Cheng go deeply into transmission lines, quarter wave impedence those kind of things. I studied the Cheng's book and I am trying to learn the parts that are skipped from the Cheng's book by studying David Griffiths' book. I am very surprised that they are quite different, people need to study both!!! This particular thread really has a lot to do with EM interference and signal integrity, Some books do talk about this kind of things and I was lucky that one of the company I worked for 10 years ago actually hired a very well known EM shielding specialist called Chris Kindle( spelling ?) to give us a two day course on grounding and shielding.

Right now I am struggling on the topics on dielectrics and magnetic materials where in EE books just assume we use homegeneous, isotropic and linear materials!!! Still learning the free current vs bounded currents and also free and bounded charges!!!

I am not familiar with microwave oven. But I think there are non metalic "so so" conductor film that can be deposit onto the surface. I am not sure as I said I am not familiar.

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Right now I am struggling on the topics on dielectrics and magnetic materials where in EE books just assume we use homegeneous, isotropic and linear materials!!! Still learning the free current vs bounded currents and also free and bounded charges!!!

I am not familiar with microwave oven. But I think there are non metalic "so so" conductor film that can be deposit onto the surface. I am not sure as I said I am not familiar.
Thank you all for the replies. So, basically, a floating shield is not really a shield.

Yungman, try reading books dedicated to material science, such as "Electronic Properties of Materials" by Rolf E. Hummel. E&M studies never go deep into the quantum physics that are required to describe nonlinear and non-isotropic phenomena. That book talks about very exotic, futuristic materials.

I understand all of the arguments about the floating shield not being a shield, but what if we have a shield that is tied to the negative end of a battery, and an AC generation circuit exists that is powered by the same battery? This is the shielded design that Morrison says is immune from external fields and keeps all fields internal.

My questions are not application-specific. I am simply looking for theoretical explanations. We may consider ideal situations; I am not yet looking to solve a real-world problem. I just want to have a very good grasp of the fundamentals, even though I went to 4 years of EE schooling =)

Thank you all for the replies. So, basically, a floating shield is not really a shield.

Yungman, try reading books dedicated to material science, such as "Electronic Properties of Materials" by Rolf E. Hummel. E&M studies never go deep into the quantum physics that are required to describe nonlinear and non-isotropic phenomena. That book talks about very exotic, futuristic materials.

I understand all of the arguments about the floating shield not being a shield, but what if we have a shield that is tied to the negative end of a battery, and an AC generation circuit exists that is powered by the same battery? This is the shielded design that Morrison says is immune from external fields and keeps all fields internal.
Think of this, the -ve end of the battery can be consider "ground". When people talking about grounding, they talk about return path. I think the word grounding is just when people tide one side of the circuit to the earth ground for safety. You really don't talk about voltage polarity with grounding. If you tide the +ve end of the battery to the ground, you have a -ve voltage supply instead. In your case, you just use the -ve side as the return path and can be used as a shield. If you tide the -ve to the earth ground, then that is grounding. But really grounding is just a common word for return path and true "grounding" to the earth is nothing more than for safety.
My questions are not application-specific. I am simply looking for theoretical explanations. We may consider ideal situations; I am not yet looking to solve a real-world problem. I just want to have a very good grasp of the fundamentals, even though I went to 4 years of EE schooling =)
Think of the electric field inside cause the charge at the inner surface of the shield, if the shield is floating, the opposite charge will appear at the out surface. The result is the floating shield almost disappeared. ( but you have to read the book on the part of the information of the shape of the charge body inside is lost ). If you assume the inner field generator is the +ve side of the battery, and if you tide the shield to the -ve side, then the charge induced on the shield can return to the battery and not going out into the space as if the shield is floating.

I design all the circuits for the Time of Flight mass spectrometer. We use a lot of high voltages for lens to deflect the ions. The way I did it is first to define a system ground and tide to earth ground for safety. Then if we want to have a negative 5KV lens, we tide the +ve of the HV DC to DC converter to the system ground. When we need a +10KV lens, we just tide the -ve to the system ground. Then we use the system ground for any shielding. I fact in some case, I float a whole microprossor system onto 15KV to control a 5 KV supply on to of the 15KV. We use the +ve 15KV to form a box and call it a floating ground!!!

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