The field at the surface of a conductor is always $\frac{\sigma}{\epsilon_0}$.
An infinite conducting plane has two faces, each with a surface charge density $\sigma$.
The field at the surface is $\frac{\sigma}{\epsilon_0}\hat{y}$, then zero inside the plate and then $\frac{-\sigma}{\epsilon_0}\hat{y}$.
This satisfies boundary conditions as the value of the field goes down by $\frac{\sigma}{\epsilon_0}$ at every interface with a free charge density $\sigma$.
Fair enough.
But when we have an infinite plane sheet of charge, the field is $\frac{\sigma}{2\epsilon_0}$. Obviously, this cannot be a conducting surface, which means it must be a dielectric and that this charge is bound. In this case, the electrostatic boundary conditions say that the field below the sheet must be the same. But it goes down by $\frac{\sigma}{\epsilon_0}$
Now my question, why is this so?
I think that there might be another field inside the infinite plate that satisfies boundary conditions, but I can't think of what kind of field this might be or what its magnitude could be. Some help?
