I Why does a conducting slab double a uniform incident field?

[OmegaKV]

For a conducting sheet that is transverse to a constant uniform incident field, I believe the resulting total field would simply be the incident field doubled. I'm trying to figure out why this happens, preferably avoiding the method of images since I am using this to figure out how the method of images works.

What I have so far: The incident field will push positive charges in the sheet in the same direction that the incident field is pointing, and pull the sheet's negative charges opposite to the direction the incident field is pointing. It's clear from this that the sheet's presense will strengthen the field, but how do you know how much it strengthens the field? It seems to me that as long as the field due to the conducting sheet is transverse to the surface of the sheet, it is consistent with gauss's law, regardless of the magnitude.

 

[cnh1995]

It's clear from this that the sheet's presense will strengthen the field,

It's exactly the opposite.

The incident field will push positive charges in the sheet in the same direction that the incident field is pointing, and pull the sheet's negative charges opposite to the direction the incident field is pointing...

...which makes the net field inside the conducting sheet zero . The field due to rearrangement of the charges on the sheet (called 'induced charges') is in direct opposition with the incident field. Hence, electric field inside a conductor is always zero in electrostatic equilibrium.

 

[OmegaKV]

Sorry I meant the field outside of the conductor. I will draw a picture for clarity.

The yellow dots are negative charges and the purple dots are positive charges, and the field inside the conductor is zero. For an incident electric field pointing downward, how does the horizontal sheet affect the field outside of the conductor?

 

[Chandra Prayaga]

It does not. The charge density σ on the surface of the conductor adjusts itself so that it is given by σ = E/ε₀, where E is the electric field outside and ε₀ is the usual constant.