Electric field inside conductor

[jd12345]

electric field "inside" conductor

Well consider a conductor with a void inside it. An external constant electric field is applied across it.

I would like to distinguish between two things : when i say "inside" the conductor i mean the void, the empty space which contains nothing but air and
when i say "in" the conductor i mean the the metal which has loads of free electrons inside it

So i fully understand why the electric field "in" the conductor becomes zero. Th electrons will rearrange themselves to cancel it . But why would the electric field "inside" the conductor become zero. IT has no free electrons and the electric field would remain as it is in that free space. Only "in" the metal should the electric field become zero

When electric field is applied all the electrons "in" the metal would start to move and rearrange themselves until they feel no force so electric field "in" the metal becomes zero
But there are no free electrons "inside" the conductor - so electric field remains as it is there

I hopei'm clear

 

[tiny-tim]

hi jd12345!

… But why would the electric field "inside" the conductor become zero. IT has no free electrons and the electric field would remain as it is in that free space. Only "in" the metal should the electric field become zero

When electric field is applied all the electrons "in" the metal would start to move and rearrange themselves until they feel no force so electric field "in" the metal becomes zero
But there are no free electrons "inside" the conductor - so electric field remains as it is there

you mean that if there was free space with a non-zero electric field,

and you put this conductor into that space, then by the principle of superposition, why isn't the field inside the conductor the same non-zero field as before?

because the non-zero field in the free space affects the charge distribution (the electrons) on the outside surface of the conductor, so when you "superpose", you're not "superposing" the same field of the conductor as in the zero-field case

 

[Hassan2]

...

I hopei'm clear

You are very clear as this is a common question. There are mathematical explanations to this question. One is based on the Laplace equation for the electric potential within the void with a constant potential on its boundary. since there is no free charge inside the void, the solution is a constnt potential all through the void and this means zero electric field.

I can't understand tiny-tim's answer, but it seems to be a mathematical explanation too.

However I think you are looking for a more physical explanation. Then this explanation may help:
Imagine two points on the boundary of the void. To move a charge from one point to the other "through the conductor", zero work is requited because they have the same potential. Now you can chose any path between the two points "through the void". Again zero work is required. This means the the work done on the charge by the field is zero. This in turn means the field ( which applies the force) is zero OR its component along the path changes direction so that the net work done by the field along the path is zero. I think its easy to prove that the latter is possible only when there is free charge in the void ( I have no solid proof now).

 

[acpower89]

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