Electric field in a region is given by $E=-4x\hat{i}+6y\hat{j}$, find the charge enclosed in cube of side $1$ m oriented as shown in figure.

Q. Electric field in a given by $\overrightarrow{E}$ = $-4x\hat{i}+6y\hat{j}$. Then find the charge enclosed in the cube of side $1$m oriented as shown in the diagram.

Q. Electric field in the space is given as $\overrightarrow{E}=2x\hat{i}+y\hat{j}$, then charge enclosed inside cube of side length $2m$ as shown in figure will be

Q. A hollow cylindrical box of length $1m$ and area of cross-section $25c{m}^2$ is placed in a three dimensional coordinate system as shown in the figure. The electric field in the region is given by $\overrightarrow{E}=50x\hat{i}$, where $E$ is in $N{C}^{-1}$ and $x$ is in metres.
Find
(i) Net flux through the cylinder.
(ii) Charge enclosed by the cylinder.

Q. An electric field given by $\overrightarrow{E}=4\hat{i}-(3y^2+2)\hat{j}$ pierces Gaussian’s cube of side $1m$ placed at origin such that its three sides represents $x,y$ and $z$ axes. The net charge enclosed within the cube is given by $-n{\epsilon }_0$. Find the value of $n$.

Q. Electric field in the region is given by $\overrightarrow{E}=(2\hat{i}+3\hat{j}+4\hat{k}){\text{NC}}^{-1}$ . The flux associated with a square plate of side $5\text{cm}$ as shown in the figure is