Two-point charges, each of magnitude $q$, are kept at the centre of the cube $O$ and vertex $A$. Find the flux through the shaded face.

The figure below shows an imaginary cube of side $a.$ A uniformly charged rod of length $\frac{a}{2}$ moves towards the right at a constant speed $v.$ At $t=0,$ the right end of the rod just touches the left face of the cube. Plot a graph between electric flux $\left({\varphi }_{\mathrm{E}}\right)$ passing through the cube versus time $\left(t\right)$.

The figure shows a cube of side $l$ with edges parallel to the axes. The electric field is in positive $y$ direction but its magnitude changes such that it is $\frac{15}{{\epsilon }_0{l}^2}$ at the bottom face and $\frac{5}{{\epsilon }_0{l}^2}$ at the top face in SI units. Find the charge enclosed by the cube.

Consider the charge configuration and spherical Gaussian surface as shown in the figure. When calculating the flux of the electric field over the spherical surface, the electric field is due to

Electric charge is uniformly distributed along a long straight wire of radius $1 \mathrm{mm}$. The charge per cm length of the wire is $Q \mathrm{C} {\mathrm{cm}}^{-1}$ Coulomb. Another cylindrical surface of radius $50 \mathrm{cm}$ and length $1 \mathrm{m}$ symmetrically encloses the wire as shown in the figure. The total flux passing through the cylindrical surface is

In the figure shown, a hemispherical bowl of radius $R$ is shown. Electric field of intensity $E$ is present perpendicular to the circular cross section of the hemisphere. The electric flux through the hemisphere is