# electric field inside a conductor

#### Wizzard_268

Joined Dec 8, 2006
2
Hello!

I'm having problems understanding some things about the electric field inside a conducture.

1)
First of all, the electric field inside a conducture is suposed to be zero in a STATIC SITUATION. What does that mean - that the electrons do not move or that the whole conductor does not move even when exposed to an outside electric field?

For a charged conducter the situation is clear. The electrons repel each other, race to the surface and create a 0 electric field inside the conductor.(if I'm wrong please correct me)

But what if the conductor (let's say a metal sphere) is exposed to an external electric field (say to a uniform field from a positively charged plate)?

2)
Would the whole sphere move or stand in place? It should move, right?

3)
How can E be 0 in the sphere? The electrons would move to one side and the force on them has to be 0. But what causes the force which opposes the one caused by the charged plate? To some extent probably the positively charged particles. But what if the external field is too big? The number of positively charged particles is limited after all and the force they exert is therefore also limited, right?
Is this the case when the lightnig strikes? But if this happens then the field inside the sphere again can't be 0. Ant the external field also doesn't reduce to zero becaude there is simply not enough electrons in the sphere to neutralize the ones on the plate if it is considered to be large.
Now that the sphere is missing electrons it would definitely move, right?

I've been turnig around in circles like this for quite some time
If anyone could shed any light on this I would be very greateful.

Thanks

#### Wizzard_268

Joined Dec 8, 2006
2
Oh and another thing.

When the sphere becomes positively charged because of the "escape" (the lightning) of electrones the sphere starts moving. But what if we were to place a particle inside such a moving sphere. Would it move with respect to the sphere or would it only move together with the sphere with respect to the charged plate but not with respect to the sphere itself?

#### Dave

Joined Nov 17, 2003
6,969
I'm having problems understanding some things about the electric field inside a conducture.

1)
First of all, the electric field inside a conducture is suposed to be zero in a STATIC SITUATION. What does that mean - that the electrons do not move or that the whole conductor does not move even when exposed to an outside electric field?

For a charged conducter the situation is clear. The electrons repel each other, race to the surface and create a 0 electric field inside the conductor.(if I'm wrong please correct me)

But what if the conductor (let's say a metal sphere) is exposed to an external electric field (say to a uniform field from a positively charged plate)?
My following discussion assumes a hollow metal sphere.

When an electric-field is applied to the sphere the free electrons within the metal sphere will react by moving to either the internal surface of the sphere or the external surface of the sphere dependant on the e-field applied - this typically takes pico-seconds (10^12 seconds). At this point the mobile charge available for conduction of current within the sphere reside entirely on the surface at equal and opposite potentials, there is no free charge residing within the metal. It should be stressed that the internal and external surfaces of the sphere are equipotentials (i.e. the potential at the surface is equal all over). The absence of free charge within the metal prevents an electric field from developing within the material. Contrast this with a dielectric which has little/no free charge and hence doesn't experience charge migration as described above - however the dielectric material experiences polarisation which enables the set up of an electric field within the dielectric material.

An important property of the electric field is that it starts on a positive charge potential and finishes on a negative charge potential, i.e. the force implicitly acts from positive to negative (although there two charge potentials in fact act on ecah other as equal and opposite forces). The sphere will respond to an electric field in accordance with the above statement.

Would the whole sphere move or stand in place? It should move, right?
The electric field would apply a force and assuming there is nothing preventing the sphere from moving it would experience a movement due to the force applied. See above.

How can E be 0 in the sphere? The electrons would move to one side and the force on them has to be 0. But what causes the force which opposes the one caused by the charged plate? To some extent probably the positively charged particles. But what if the external field is too big? The number of positively charged particles is limited after all and the force they exert is therefore also limited, right?
Is this the case when the lightnig strikes? But if this happens then the field inside the sphere again can't be 0. Ant the external field also doesn't reduce to zero becaude there is simply not enough electrons in the sphere to neutralize the ones on the plate if it is considered to be large.
Now that the sphere is missing electrons it would definitely move, right?

I've been turnig around in circles like this for quite some time
If anyone could shed any light on this I would be very greateful.

Thanks
The best way to think about why the e-field inside the sphere is zero is to consider the internal surface of the sphere being a surface, exactly the same as a suface of a flat plate. The positive or negative charge (discussed above) resides on this surface. Now if you close this surface as is the case with the internal surface of the sphere then the surface potential at all point inside the surface is equal (i.e. an equipotential) - therefore given that "the electric field is that it starts on a positive charge potential and finishes on a negative charge potential", it should be clear that this cannot be the case for an equipotential and hence the electric field inside the sphere must be zero. Another important aspect of this is that the electric field vector must intersect the surface of the sphere at right-angles, and no other angle - however this is not particularly relevant in the context of your initial query.

Apologies if there are any part of what I have said that are confusing. Post back any problems and I will try to explain better.

Dave

#### suniltdpa

Joined Dec 8, 2006
2
Hi,
I need to find out the electric field inside the conductor.

#### Dave

Joined Nov 17, 2003
6,969
Hi,
I need to find out the electric field inside the conductor.
There isn't one - read my previous post.

When an electric-field is applied to the conductor the free electrons within the metal conductor will react by moving to either the internal surface of the conductor or the external surface of the conductor dependant on the e-field applied - this typically takes pico-seconds (10^-12 seconds). At this point the mobile charge available for conduction of current within the conductor reside entirely on the surface at equal and opposite potentials, there is no free charge residing within the conductor. It should be stressed that the internal and external surfaces of the conductor are equipotentials (i.e. the potential at the surface is equal all over). The absence of free charge within the conductor prevents an electric field from developing within the material.
This is the case for a conductor under electrostatic conditions.

Dave

#### Dave

Joined Nov 17, 2003
6,969
...this typically takes pico-seconds (10^-12 seconds).
In fact Serway and Beichner state that it takes 10^-16 seconds to establish electrostatic equilibrium.

Dave