Two infinite plane sheets $A$ and $B$ are shown in the figure. The surface charge densities on $A$ and $B$ are $\left(\frac{2}{\mathrm{\pi }}\right)\times {10}^{-9} \mathrm{C} {\mathrm{m}}^{-2}$ and $\left(\frac{-1}{\mathrm{\pi }}\right)\times {10}^{-9} \mathrm{C} {\mathrm{m}}^{-2}$ respectively. $C$, $D$ and $E$ are three points where electric fields (in $\mathrm{N} {\mathrm{C}}^{-1}$) are $E_{\mathrm{c}}$, $E_{\mathrm{D}}$ and $E_{\mathrm{E}}$ respectively.

  

    

A surface has the area vector $\overrightarrow{A}=\left(2\hat{i}+3\hat{j}\right) {\mathrm{m}}^2$. What is the flux of a uniform electric field through the area if the field is$\overrightarrow{E}=4\hat{\mathrm{k}} \mathrm{N} {\mathrm{C}}^{-1}$?

An electric field given by $\overrightarrow{E}=4.0\hat{\mathrm{i}}-3.0\left(y^2+2.0\right)\hat{\mathrm{j}}$, pierces a Gaussian cube of edge length $2.0 \mathrm{m}$ and positioned as shown in the figure. (The magnitude $E$ is in newtons per coulomb and the position $x$ is in meters). What is the electric flux through the

$\left(a\right)$ top face

An electric field given by, $\overrightarrow{E}=4.0\hat{\mathrm{i}}-3.0\left(y^2+2.0\right)\hat{\mathrm{j}}$ pierces a Gaussian cube of edge length $2.0 \mathrm{m}$ and positioned as shown in the figure. (The magnitude $E$ is in newtons per coulomb and the position $x$ is in meters). What is the electric flux through the

(b) bottom face

An electric field given by, $\overrightarrow{E}=4.0\hat{\mathrm{i}}-3.0\left(y^2+2.0\right)\hat{\mathrm{j}}$ pierces a Gaussian cube of edge length $2.0 \mathrm{m}$ and positioned as shown in the figure. (The magnitude $E$ is in newtons per coulomb and the position $x$ is in meters) What is the electric flux through the left face.

An electric field given by, $\overrightarrow{E}=4.0\hat{\mathrm{i}}-3.0\left(y^2+2.0\right)\hat{\mathrm{j}}$ pierces a Gaussian cube of edge length $2.0 \mathrm{m}$ and positioned as shown in the figure. (The magnitude $E$ is in newtons per coulomb and the position $x$ is in meters). What is the electric flux through the back face?

An electric field given by $\overrightarrow{E}=4.0\hat{\mathrm{i}}-3.0\left(y^2+2.0\right)\hat{\mathrm{j}}$ pierces a Gaussian cube of edge length $2.0 \mathrm{m}$ and positioned as shown in the figure. (The magnitude $E$ is in newtons per coulomb and the position $x$ is in meters). What is the electric flux through the cube?

The cube in figure has edge length $\sqrt{2} \mathrm{m}$ and is oriented as shown in a region of the uniform electric field. Find the electric flux through the right face, if the electric field in newtons per coulomb, is given by,$6.00 \hat{\mathrm{i}}$.