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I know that the electric field is zero inside a conductor. However, a plate does not have some kind of "interior space." So, if there is a infinitely large conductor plate with a uniform charge density, what is the electric field made by the plate? Is it just the same as a plate with uniform charge distribution? It is so much confusing...

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  • $\begingroup$ An infinitely large plate with a finite net change has a charge density of zero and no electric field. Maybe change it to a charge density of $\sigma$ instead of a net charge of $Q$. $\endgroup$ – Ben51 Jan 17 '18 at 13:30
  • $\begingroup$ Ok I will edit it. What is the answer then? Could you tell me? $\endgroup$ – Keith Jan 17 '18 at 13:31
  • $\begingroup$ The field only cares where the charges are, not whether they’re in a conductor or not. So it’s the same. But in general, you’re not allowed to specify the distribution of charge on a conductor: it will rearrange itself to eliminate the field inside and make the field just outside normal to the surface. $\endgroup$ – Ben51 Jan 17 '18 at 13:36
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The electric field from an infinite single plane of charge is given by $$\vec{E}=\frac{\sigma}{2\epsilon_0}\hat{n},$$ where $\sigma$ is the area charge density and $\hat{n}$ is the unit vector normal to the plane and away from the plane on both sides.

A conducting plate necessarily has 2 planes of charge because to be a conductor it must be material object with 2 different sides. The charge will rearrange until there is a plane of charge on each side of the plate. At some distance away from the surface, the net electric field will be the sum of the fields which will be $$\vec{E}=\frac{\sigma}{\epsilon_0}\hat{n}.$$

While there is no truly infinite plate, if the distance from the plate (or the planes) is small compared to the size of the plate, these relationships are very good approximations, especially if one is not close to the edge of the plates.

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If you refer to an ideal plate, with zero width, it's right that there is no "internal space", and so there is no point on asking what is the electric field in that space.

Said so, if with an "infinitely large conductor" you mean a conductor which cover the entire universe, the electric field inside it will be zero, and nothing will exist outside it.

In a more real-world example, let's pick a square plate with it's width: inside it the electric field will be zero, and outside it will be perpendicular to the surface only in the real proximity of the plate

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