The electric field in a certain region of space $\left(5\hat{\mathrm{ı}}+4\hat{\mathrm{j}}-4\hat{\mathrm{k}}\right)\times {10}^5{\mathrm{NC}}^{-1}$. Calculate electric flux due to this field over an area of $\left(2\hat{\mathrm{i}}-\hat{\mathrm{j}}\right)\times {10}^{-2}{\mathrm{m}}^2$.

A charge $q$ is situated at the centre of an imaginary hemispherical surface, as shown in Fig. Using Gauss's theorem and symmetry considerations, determine the electric flux due to this charge through the hemispherical surface.

A hollow cylindrical box of length $1 \mathrm{m}$ and area of cross-section $25 {\mathrm{cm}}^2$ is placed in a three-dimensional co-ordinate system as shown in Fig. The electric field in the region is given by $\overrightarrow{E}=50 x\hat{i}$,

Where E is in ${\mathrm{NC}}^{-1}$ and $x$ is in meters.

Find net flux through the cylinder

A hollow cylindrical box of length $1 \mathrm{m}$ and area of cross-section $25 {\mathrm{cm}}^2$ is placed in a three-dimensional coordinate system as shown in Fig. 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 charge enclosed by the cylinder.