1. Jun 9, 2007

### sunchips

i heard that a faraday cage is often used in shielding e.g. sensitive electrical equipment. I was just wondering, because, in http://socrates.berkeley.edu/~fajans/Teaching/cartoons/Shielding/TestChargeShielding_files/frame.htm

it seems that the electric field is not zero at ALL times. i.e. there is an interval of time where an electric field does exist inside the cage, before the charges redistribute themselves.

I was just wondering then, for the "shielding" application of the cage, that at that interval of time, couldnt the short-lived electric field still affect sensitive electrical eqipment housed inside? or is the above wrong, and there is another explanation that says that the electrical field is zero at ALL tiems.

Thanks so much!

2. Jun 9, 2007

### smallphi

Electric field cannot penetrate a conductor only in electroSTATICS. That means your suspicion was right - only after the short time necessary for the charges to redistribute, the field inside the conductor becomes zero.

In non-static situations, the electric field inside conductor is not zero at all. Take an electric circuit for most blatant example. If there is a device that maintains potential difference between two points in a conductor, the electric charges will start moving trying to kill the electric field, thus creating a current. They won't be able to kill the field cause the battery is constantly pumping energy. The moment you remove the battery though, the charges redistribute for a short time and the field is zero.

Last edited: Jun 9, 2007
3. Jun 9, 2007

### ice109

absolutely false, a faraday cage will cancel all e fields of some frequencies depending on the thickness of cage. a wire is not a faraday. a faraday cage is hollow conductor

4. Jun 9, 2007

### smallphi

A high enough frequency penetrates Faraday cage since the electrons can't move fast enough to neutralize the field so what exactly is false in my statement?

5. Jun 9, 2007

### ice109

no a high enough frequency penetrates the cage because its skin depth is very low

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6. Jun 9, 2007

### smallphi

The skin depth is low because the electrons can't move fast enough to neutralize the field. The dept of penetration of electric field inside a conductor, the so called skin depth, depends on the frequency of the field and on the conductivity of the material. The conductivity is a measure how fast the electrons can move in the material.

Last edited: Jun 9, 2007
7. Jun 9, 2007

### ice109

drift velocity is not the same thing as the propagation of the EM wave. the electrons cancel the field out at the speed of light.

Last edited: Jun 9, 2007
8. Jun 9, 2007

### smallphi

Absolutely false!

Look at a derivation of skin depth. The conductivity, sigma, enters the Maxwell equations through the Om's law: J(current density)= sigma x E (electric field). In that equation sigma represents the ability of the electrons to move against the resistance of the material.

If the electric field is not an idealized plane wave, it varies with position and time. The electrons have to create an excess charge at places where the field is high to cancel it out. An excess charge is not created at the speed of light as you claim because the electrons have to travel macroscopic distances and their speed in conductors is not the speed of light nor is infinite.

Last edited: Jun 9, 2007
9. Jun 9, 2007

### ice109

1 you keep changing your post, stop doing that
2 you're being very vague with your language so it is difficult to refute you
3 you do realize skin depth increases with resisitivity right?

this is the equation for skin depth for good conductors

$$\delta \approx 503 \sqrt{\frac{\rho}{\mu _r f}}$$

notice resistivity is on top.

4 i was wrong about them moving the speed of propagation of the wave to cancel it but they don't need to. they can move the drift velocity and that is plenty fast enough. you're thinking too macroscopically. the electrons are not moving meter or centimeters or even millimeters to cancel the EM wave, they're moving the amplitude of the wave which is very small.

Last edited: Jun 9, 2007
10. Jun 9, 2007

### smallphi

Conductivity is the reciprocal of resistivity. Big conductivity, sigma, means bigger speeds of electrons, smaller resistivity rho, smaller skin depth. Hence bigger speeds of electrons mean smaller penetration of the field just as I claimed.

The inhomogeneities of the electric field have macroscopic extent. It's impossible for the electrons to move a microscopic distance, yet create an excess charge of macroscopic extent to cancel the field.

Even if the electrons don't have to move a lot, in the case of perfectly homogeneous field, their speed is still governed by the conductivity sigma which is seen by the way sigma enters the Maxwell equations in the derivation of skin depth. It enters through Ohm's law J = sigma E, in which sigma is a measure of how fast the electrons can move in that material. So claiming that the cancelation of the electric field has nothing to do with how fast the electrons can move because they move 'just a little' is plain ridiculous.

Last edited: Jun 9, 2007
11. Jun 9, 2007

### ice109

you initial post says that faraday cages only work in electrostatic situations , and not in changing fields, do you stand by this or not?

12. Jun 9, 2007

### smallphi

That is what you made of my post, not what it says.

13. Jun 9, 2007

### ice109

14. Jun 9, 2007

### sunchips

just for amusement, are smallphi and ice109 enemies/rivals? :P

15. Jun 10, 2007

### Jack111

As the demonstration on that berkely website shows, in the static case metals shield electric fields from their interior. Anyone familiar with gauss's theorem in electrostatics might like to consider a gaussian surface throughout the interior of the hollow conductor enclosing the cavity to see this.

In the dynamic case things are not so simple. EM waves mostly reflect from metals but a portion of them will continue into the metal, although they are rapidly attenuated on a distance scale called the skin depth, see for example http://en.wikipedia.org/wiki/Skin_depth, so that a portion of the incident radiation will penetrate the conductor (although for any macroscopic cage this will be a VERY small portion, as the diagram on the wikipedia article shows).

However, this model is only appropriate up to a certain point. Consider for example gamma rays, which have no problem clearing several centimetres of lead. This is because their frequency is of the order of 10^19 Hz or more. On these timescales the metal no longer acts as a conductor since the microscopic parts of the metal respond far too slowly to move currents around in response to field changes. Indeed, our 'metallic' assumption was that 1 << sigma / (epsilon0 * omega), which begins to look very shaky for omega in the gamma ray regime.

Consequently, very high frequency fields can and do penetrate faraday cages

Also with regard to the current in conductors questions posed above, electrons don't move fast at all in conductors, it's the electromagnetic waves that move fast (how fast the electrons 'notice the other ones moving') which typically travel at ~75% of c (the difference being due to refractive indices or something)