How can the electric field inside a conductor be zero?

[ycheng18]

I know there is a lot of answers out there, but so far none really answered my question.

Say I have this radioactive conductor sphere that has a negative charge. Of course, all the negative charges will be spread evenly on the surface and there SHOULD be 0 electric field inside the conductor. If this radioactive conductor now decays, and produces an alpha particle (which has a +2e charge), shouldn't the produced alpha particle move? As long as it is not in the dead center of a sphere, it should be attracted to one of the sides due to negative attraction force. If the particle moves because of the charge of the sphere, doesn't it suggest that there is an electric field that is moving the positive charge, and therefore suggests there IS an electric field?

 

[haruspex]

I know there is a lot of answers out there, but so far none really answered my question.

Say I have this radioactive conductor sphere that has a negative charge. Of course, all the negative charges will be spread evenly on the surface and there SHOULD be 0 electric field inside the conductor. If this radioactive conductor now decays, and produces an alpha particle (which has a +2e charge), shouldn't the produced alpha particle move? As long as it is not in the dead center of a sphere, it should be attracted to one of the sides due to negative attraction force. If the particle moves because of the charge of the sphere, doesn't it suggest that there is an electric field that is moving the positive charge, and therefore suggests there IS an electric field?

The off-centre positive charge of the alpha particle will create an asymmetric field within the sphere. This will disturb the charges on the surface, causing them to redistribute. Now there is a field within the sphere due to the surface charge. The alpha particle then accelerates...

 

[ycheng18]

"Now there is a field within the sphere due to the surface charge"

So does this mean there can be electric fields inside a hollow charged conductor?

 

[Student100]

"Now there is a field within the sphere due to the surface charge"

So does this mean there can be electric fields inside a hollow charged conductor?

If the charge on the surface of the hollow charged conductor is not uniformly distributed, then yes.

 

[ycheng18]

If the charge on the surface of the hollow charged conductor is not uniformly distributed, then yes.

So whenever I add a charge inside the hollow conductor, the charge will be disrupted and an electric field will form? If yes, then when I add a positive test charge (electric field test) to the hollow sphere, shouldn't the test charge move? If that is the case, how can you argue there is 0 electric field inside the hollow conductor?

 

[Student100]

So whenever I add a charge inside the hollow conductor, the charge will be disrupted and an electric field will form? If yes, then when I add a positive test charge (electric field test) to the hollow sphere, shouldn't the test charge move? If that is the case, how can you argue there is 0 electric field inside the hollow conductor?

Maybe I should clarify the above:

There's always an electric field (in easy symmetrical cases it's vector sum is 0 anywhere inside the shell), even with uniformly charged hollow non conducting/conducting shells. Are you confusing Flux with fields?

To maybe answer your question, if your shell is a conductor and you added a positive test charge off center, the charges on the surface of the conductor would redistribute, the vector sum of the field lines would no longer add up to be zero due to the asymmetrical surface charge, and your test charge would certainly begin to move.

 

[ycheng18]

Maybe I should clarify the above:

There's always an electric field (in easy symmetrical cases it's vector sum is 0 anywhere inside the shell), even with uniformly charged hollow non conducting/conducting shells. Are you confusing Flux with fields?

To maybe answer your question, if your shell is a conductor and you added a positive test charge off center, the charges on the surface of the conductor would redistribute, the vector sum of the field lines would no longer add up to be zero due to the asymmetrical surface charge, and your test charge would certainly begin to move.

Well, we've just started to learn electrical fields 2 weeks ago (I am in 2nd year IB HL Physics). I don't really know what a flux is either. I was just confused about how it is possible that the textbook/teacher says "there is no electric field inside a hollow sphere". But I guess this is a topic that is too advanced for me currently, I might revisit this when I learn about more advanced stuff (maybe later in the year or in college). But thank you for answering my question.

 

[haruspex]

the textbook/teacher says "there is no electric field inside a hollow sphere".

Strictly speaking, that is a statement about electrostatics. The set-up you described is not static.
If you were somehow to fix the alpha particle at some point within the sphere, the charges on the surface would quickly rearrange so as to exactly counter the field from the alpha particle. So it would very soon again be the case that there is no field inside the spherical shell [edited: I previously wrote "sphere" by mistake]. But that is from adding the two fields together, the one from the particle and the one from the sphere's surface.
The alpha particle itself does not feel its own field, only that from the spherical shell. Since the shell's charges are no longer uniformly distributed, there is a field from that. With the alpha particle allowed to move, it will accelerate towards the nearest point on the shell, with the shell's field constantly shifting to match.

 

[Aaron Crowl]

A real conductor can in fact have an electric field inside.

When you study electrostatics you begin by considering ideal materials like a perfect conductor. If an electric field appeared inside a perfect conductor you would have an infinite current. So you are taught that conductors cannot have a field inside. A realistic conductor has some resistance to it and fields can penetrate to a small degree.

Also, consider that your radioactive situation is a dynamic scenario and not a static one. Charges will move to the surface of a conductor to cancel out any fields that would appear inside the conductor. A perfect conductor will do this instantly.

So you might ask "Why would we say that electric fields cannot penetrate conductors if it's more complicated than that?" The reason is that this a good approximation which generates good results while simplifying the physics.

 

[Dale]

I was just confused about how it is possible that the textbook/teacher says "there is no electric field inside a hollow sphere".

As @haruspex mentioned the complete statement is that there is no electric field inside an electrostatic conductor. The electrostatic condition is very important to pay attention to.

The general point is that physicists, like everyone, are a little lazy and want to take shortcuts whenever possible. Calculating the field inside an object is generally difficult, but if the object is in an electrostatic situation and the object is a conductor then we can take a huge shortcut: the field is zero.

 

[jartsa]

For some reason you all seem to be getting something wrong.

Is it not like this:

When the conducting sphere is filled with any non-conducting material, then there can be an electric field in that material.

When the conducting sphere is filled with any conducting material, then there can not be an electric field in that material.

 

[Dale]

When the conducting sphere is filled with any conducting material, then there can not be an electric field in that material

Only in the electrostatic condition.

 

[Vanadium 50]

First, what has been said up to now is correct.

Second, the premise is not. An alpha particle does not appear out of nowhere. You have a +2 alpha moving away from the -2 ion that it left behind. The alpha is actually moving quite slowly - about 10% of the speed of changes in the electric field. So the sea of electrons in the conductor react very quickly to cancel out the changes in the configuration caused by the alpha decay. So in fact what happens is actually very close to the electrostatic condition.

 

[jartsa]

First, what has been said up to now is correct.
Second, the premise is not. An alpha particle does not appear out of nowhere. You have a +2 alpha moving away from the -2 ion that it left behind. The alpha is actually moving quite slowly - about 10% of the speed of changes in the electric field. So the sea of electrons in the conductor react very quickly to cancel out the changes in the configuration caused by the alpha decay. So in fact what happens is actually very close to the electrostatic condition.

So the alpha particle is pulled to the wall. And that's because the alpha attracts electrons to the part of wall closest to the alpha, and then those electrons attract the alpha. So there is an electric field accelerating the alpha. Right?

So in an electrostatic condition there is a field, and in the opposite case there would be no field. That's a little bit confusing.

EDIT: This was wrong:
Shouldn't that be the other way around? If the alpha was much more dynamic, then the electrons would stay static, and that I would call the electrostatic condition.

 

[Vanadium 50]

The alpha only moves maybe 100 microns before it stops. It feels a large force from the ion it left behind. More importantly all the nearby free charges feel these forces and very very quickly reconfigure themselves to oppose both charges. The wall is very, very far away, and by the time it can react to the change in conditions, this change is no longer relevant.

 

[haruspex]

The alpha only moves maybe 100 microns before it stops. It feels a large force from the ion it left behind. More importantly all the nearby free charges feel these forces and very very quickly reconfigure themselves to oppose both charges. The wall is very, very far away, and by the time it can react to the change in conditions, this change is no longer relevant.

I would not get hung up on the details of the creation and motion of the alpha particle. The question is really about what would happen if a positive charge could magically appear within the hollow of the sphere (and not dead-centre). The alpha particle was just an attempt to frame it as a feasible event, but the question is valid even without that.

 

[haruspex]

For some reason you all seem to be getting something wrong.

Is it not like this:

When the conducting sphere is filled with any non-conducting material, then there can be an electric field in that material.

When the conducting sphere is filled with any conducting material, then there can not be an electric field in that material.

I'm not sure what you are saying that others have been getting wrong. Please clarify.

 

[Dale]

the question is valid even without that.

Well, @Vanadium 50 has a good objection. Charge is conserved, so you cannot just magically have charge appear, that would violate Maxwells equations as well as the conservation laws in QM. The best that you can do is have some positive and negative charge separate. The separated charges do have a much stronger interaction with each other than with any far away surface charges.

 

[haruspex]

Well, @Vanadium 50 has a good objection. Charge is conserved, so you cannot just magically have charge appear, that would violate Maxwells equations as well as the conservation laws in QM. The best that you can do is have some positive and negative charge separate. The separated charges do have a much stronger interaction with each other than with any far away surface charges.

That's a good objection to the imagined sequence by which this lone charge came to be, but the question does not require any realistic origin. It could have been written as "suppose there is a lone charge..." There is a perfectly good and illuminating answer that does not depend on the impossibility of the circumstance arising.

 

[Dale]

It could have been written as "suppose there is a lone charge...".

Yes. That would have been a valid question.

 

[jartsa]

I'm not sure what you are saying that others have been getting wrong. Please clarify.

This seems to be almost true according to you guys:

the textbook/teacher says "there is no electric field inside a hollow sphere".

While my opinion is that there is almost no truth there. Not in the electrostatic condition or otherwise.

When there are no charges inside a Faraday cage, then there is not any electric field inside that gage. That's because the fields from any outside charges do not enter the cage, in the electrostatic condition. Also the fields from charges on the gage do not enter the cage, in the electrostatic condition.

EDIT: Oh yes, when there are charges inside the cage, then fields from the charges on the cage do not cancel out each other, in the electrostatic condition.

 

[Student100]

While my opinion is that there is almost no truth there. Not in the electrostatic condition or otherwise.

There are no perfect conductors, I don't think anyone here is arguing that. There are conductors which are approximately perfect.

When there are no charges inside a Faraday cage, then there is not any electric field inside that gage. That's because the fields from any outside charges do not enter the cage, in the electrostatic condition. Also the fields from charges on the gage do not enter the cage, in the electrostatic condition.

Are you now arguing there are perfect Faraday cages? There is still electric fields inside, the fields just happen to sum to zero assuming things are in equilibrium.

EDIT: Oh yes, when there are charges inside the cage, then fields from the charges on the cage do not cancel out each other, in the electrostatic condition.

They do(The Net Fields), or it wouldn't be in an electrostatic configuration.

I'm not really sure what you're trying to argue here?

Edit: I think I wrongly attributed a post made by someone else to you, when trying to decipher what you were getting at. My mistake.

 

[Vanadium 50]

It's certainly true that if you can make charges appear and disappear at will, violating conservation laws, you can make them appear and disappear too fast for the charges in the conductor to respond. But what does that tell us about the real world? Do we really want to teach the field inside a conductor is zero - except magic?

 

[haruspex]

when there are charges inside the cage, then fields from the charges on the cage do not cancel out each other, in the electrostatic condition.

Ok, I see what you are objecting to. I did write something wrongly in my first post, now edited.
Indeed, in the simple case of a central point charge inside a hollow conducting sphere, there is no field from the sphere, by symmetry, but the field from the point charge pervades the hollow. So the teacher's blanket statement (if accurately quoted by the OP) was wrong on that basis.

Thanks for picking that up.

 

[Student100]

It's certainly true that if you can make charges appear and disappear at will, violating conservation laws, you can make them appear and disappear too fast for the charges in the conductor to respond. But what does that tell us about the real world? Do we really want to teach the field inside a conductor is zero - except magic?

Maybe I've been under the (possibly very) wrong assumption that if we brought a charge into a hollow shell, held it in place and allowed the system to obtain equilibrium, and then released the charge that the equilibrium state wouldn't remain stable in the presences of the electrostatic forces only. The charge would then move towards the shell, and we'd have a net non zero field inside the conductor.

Wouldn't that bypass the need to break conservation laws in the "lone charge brought into a shell" scenario?

 

[Vanadium 50]

If I have a hollow shell of uniform charge density, the force on a change inside is zero.

 

[haruspex]

If I have a hollow shell of uniform charge density, the force on a change inside is zero.

I assume that is in reply to post #25. I would guess Student100 meant a charge off-centre, held in place. Since the shell is a conductor and allowed to reach equilibrium, it will no longer be uniformly charged.

 

[jartsa]

There are no perfect conductors, I don't think anyone here is arguing that. There are conductors which are approximately perfect.

True.

Are you now arguing there are perfect Faraday cages? There is still electric fields inside, the fields just happen to sum to zero assuming things are in equilibrium.

I just call a situation where fields sum to zero a situation where there's no field. (And so do you, when you say there's no field around a neutral potato (or is there an electric field around a neutral potato?))

They do(The Net Fields), or it wouldn't be in an electrostatic configuration.

I say they don't. And I have a better understanding. Charged things inside a Faraday cage induce charges on the cage. Then the induced charges on the cage produce a net field inside the cage.

 

[Student100]

I just call a situation where fields sum to zero a situation where there's no field. (And so do you, when you say there's no field around a neutral potato (or is there an electric field around a neutral potato?))

You had said the fields don't penetrate the cage, which is an interpretation that can lead to confusion. I find it better to say the charge distribution of the cage would rearrange themselves in such a manner to so that the net electric field inside is zero.

I say they don't. And I have a better understanding. Charged things inside a Faraday cage induce charges on the cage. Then the induced charges on the cage produce a net field inside the cage.

Only when current is flowing, that would not be the "electrostatic configuration" when the net fields inside the cage sum to zero.

I assume that is in reply to post #25. I would guess Student100 meant a charge off-centre, held in place. Since the shell is a conductor and allowed to reach equilibrium, it will no longer be uniformly charged.

Basically the post was just how I had interpreted Earnshaw's theorem. It seemed to me to be a way for what I assumed the OP's initial question was that could be asked in a way that wouldn't require magic for the net field inside the conductor to be non-zero. As we transition from unstable equilibrium to the dynamic condition there would be a net field inside, as the charges redistribute on the surface.

 

[rude man]

So whenever I add a charge inside the hollow conductor, the charge will be disrupted and an electric field will form? If yes, then when I add a positive test charge (electric field test) to the hollow sphere, shouldn't the test charge move? If that is the case, how can you argue there is 0 electric field inside the hollow conductor?

Your ion of charge q, placed inside the shell, does generate a finite E field, and a subsequent test charge would indicate an E field. E.g. if your ion is at the center the E field would be kq/r^2 in all directions away from the center etc.

But remember that a test charge is by definition of infinitesimally small charge so if you place a test charge plus your ion in the shell, the ion is not affected.

If all you do is place your ion inside the shell you set up an E field but that E field does not impart a force on the ion. A charge of any size does not impart a force on itself!