Electric field inside a conductor

[FS98]

The electric field inside of a conductor is 0, but what exactly does inside a conductor mean? It’s easy enough to understand what this means if the conductor is closed, but what if the conductor is open in some way? What counts as inside and what doesn’t?

 

[jasonRF]

A conductor is a solid 3-dimensional object. "Inside" means inside the conducting material itself; for example inside the actual metal part of a wire, or inside a solid spherical conductor. By the way, the electric field in a perfect conductor is zero. There can be an electric field inside an imperfect conductor.

jason

 

[FS98]

A conductor is a solid 3-dimensional object. "Inside" means inside the conducting material itself; for example inside the actual metal part of a wire, or inside a solid spherical conductor. By the way, the electric field in a perfect conductor is zero. There can be an electric field inside an imperfect conductor.

jason

Is a conductor necessarily solid? How about a faraday cage?

 

[jasonRF]

The word "conductor" refers to physical material that conducts electricity well. Copper and gold would be good conductors. Plastic is an insulator, not a conductor. Silicon is neither a good conductor nor an insulator; it is a semi-conductor.

 

[jasonRF]

Is a conductor necessarily solid? How about a faraday cage?

A liquid can be a conductor - think of lead that is hot enough to be a liquid.

The metal parts of a Faraday cage are made out of conductors; there may be structural parts of a Faraday cage made of other materials (like wood) that simply hold up the metal conducting parts. Presumably the inside of the Faraday cage has air as well as some materials you want to protect, some of which may be conductors, some not.

 

[sophiecentaur]

Is a conductor necessarily solid? How about a faraday cage?

If the cage is good enough, there can be no field inside it. "Good Enough" means very nearly the equivalent of a 10m cube of copper with a 1m cubic hole cut inside it - no joints, no air holes and no wires in or out. You would not measure any field in there. Take a cheap box made of expanded metal, with riveted joints and wires running in and out. That's a different matter. Which of those would you like to discuss here?

 

[FS98]

If the cage is good enough, there can be no field inside it. "Good Enough" means very nearly the equivalent of a 10m cube of copper with a 1m cubic hole cut inside it - no joints, no air holes and no wires in or out. You would not measure any field in there. Take a cheap box made of expanded metal, with riveted joints and wires running in and out. That's a different matter. Which of those would you like to discuss here?

I’m just confused about the fact that a faraday cage has some open space where the electric field is 0. Based on some of the other comments, shouldn’t it only be the case that the electric field inside of the conducting material is 0? The air between the conducting material is not the same as the conducting material, so I’m not sure why a faraday cage would work at all, good or not.

 

[Dale]

I’m just confused about the fact that a faraday cage has some open space where the electric field is 0.

That is not a fact. The electric field can be nonzero in the open space inside an ideal Faraday cage.

I’m not sure why a faraday cage would work at all, good or not.

A Faraday cage prevents external fields from getting in, but doesn’t prevent fields from sources inside the cage.

 

[FS98]

That is not a fact. The electric field can be nonzero in the open space inside an ideal Faraday cage.

Okay, so we can only say tha

That is not a fact. The electric field can be nonzero in the open space inside an ideal Faraday cage.

A Faraday cage prevents external fields from getting in, but doesn’t prevent fields from sources inside the cage.

So could we say that the electric field must only be 0 inside the conducting material of a conductor? And what would be required for this to hold true? I’m tempted to say that the conductor must be at equilibrium, but non-electric forces can be involved that I’m pretty sure make this qualifier not the correct one.

 

[DrZoidberg]

Let's look at the generalized form of Ohm's law J=σE. (Current density = conductivity * electric field strength)
This means that E must always be equal to J/σ. So if the current is zero the field must also be zero. That tells us that in a static situation - i.e. there may be charges but no currents flowing - the field inside the material must be zero.

Here is another way to express this: If there was a field anywhere inside the conductor then a current would flow and would continue to flow until the field has reached zero.

 

[Dale]

So could we say that the electric field must only be 0 inside the conducting material of a conductor? And what would be required for this to hold true?

Yes. What is required is that the conductor be a very good conductor or that the frequency of the fields be relatively low.

 

[sophiecentaur]

Yes. What is required is that the conductor be a very good conductor or that the frequency of the fields be relatively low.

Those practical conditions apply for a realistic approach to the situation. Unfortunately, the OP seems to want to consider a 'perfect' Faraday cage. There's some incompatibility there. You cannot have the equivalent to an irresistible force and an immoveable object at the same time.
You can discourage further picking over of this corpse by suggesting that the OP tries some actual calculations . . . .

 

[Stavros Kiri]

The electric field inside of a conductor is 0

At equilibrium only, and for the total E field. J = σE , J=0, thus E=0.

Edit P.S. : just realized that this has been essentially covered already by @DrZoidberg

 

[Stavros Kiri]

So could we say that the electric field must only be 0 inside the conducting material of a conductor?

Yes (but not only); even inside an empty holow metal conductor, with the E sources outside. (Faraday cage)
[Mathematically] It is actually the uniqueness of the solution of a boundary value problem (for the potential Φ) that dictates that. [Φ=const ⇔ E=0 (E = -∇Φ, etc. ...)]

0 inside the conducting material of a conductor? And what would be required for this to hold true? I’m tempted to say that the conductor must be at equilibrium, but non-electric forces can be involved that I’m pretty sure make this qualifier not the correct one.

Equilibrium, as said. Non-electric forces don't count, because we're talking about 'Electrostatic Equilibrium'.

I’m just confused about the fact that a faraday cage has some open space where the electric field is 0. Based on some of the other comments, shouldn’t it only be the case that the electric field inside of the conducting material is 0? The air between the conducting material is not the same as the conducting material, so I’m not sure why a faraday cage would work at all, good or not.

Also explained with the above.