## Related questions with answers

A flat slab of nonconducting material has thickness $2 d$, which is small compared to its height and breadth. Define the $x$ axis to be along the direction of the slab's thickness with the origin at the center of the slab. If the slab carries a volume charge density $\rho_{\mathrm{E}}(x)=-\rho_0$ in the region $-d \leq x<0$, and $\rho_{\mathrm{E}}(x)=+\rho_0$ in the region $0<x \leq+d$, determine the electric field $\overrightarrow{\mathbf{E}}$ regions $\text{(c) } -d \leq x<0$. Let $\rho_0$ be a positive constant.

Solution

VerifiedSuppose we have a very long slab, and it has a thickness of $2d$ and charge density $\rho_E=-\rho_0$ for $-d<x<0$ and $\rho_E=+\rho_0$ for $0<x<d$, we need to find the electric field for $-d<x<0$, but first we need to draw a Gauss sphere (cylinder) inside the slab as shown in the figure:

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