Easy# Electric Fields in Dielectric Slabs

EANDM-IHVD@Z

A slab of conductor (region 1) has a thickness $a$ with a covering of dielectric (region 2) as shown in the accompanying figure. The slab and the dielectric are very large in the $\hat{y}$ and $\hat {z}$ directions.

The conductor extends over the range $0 < x < a$ in the $\hat{x}$ direction, and the dielectric extends over the range $b < x < b$ in the $\hat{x}$ direction. The conductor has no charge, and the dielectric has a polarization given by $\vec{P}(x)=C_o \hat{x}$ where $C_o$ is a constant.

What is the value of the electric field $E$ in region 2 ($a < x < b$)?