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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 ($a < x < b$)?

A

$E = \cfrac{-C_o x}{\epsilon_o}\: \text{(N/C along x)}$

B

$E = C_o \: \text{(N/C along x)}$

C

$E=0 \; \text{(N/C along x)}$

D

$E = \cfrac{-C_o}{\epsilon_o}\: \text{(N/C along x)}$

E

$E = \cfrac{C_o}{\epsilon_o}\: \text{(N/C along x)}$