$A$ charge $q$ is placed at the centre of the open end of a cylindrical vessel. The flux of the electric field through the surface of the vessel is:

How much electric flux will come out through a surface $S = 10\hat{j}$ kept in an electrostatic field $\vec{E} = 2\hat{i} + 4\hat{j} + 7\hat{k}$ units?

$A$ point charge $+10 \; \mu C$ is at a distance $5 \; cm$ directly above the centre of a square of side $10 \; cm$,as shown in the figure. What is the magnitude of the electric flux through the square?

In a region, the intensity of an electric field is given by $E = 2i + 3j + k$ in $NC^{-1}$. The electric flux through a surface $S = 10i \ m^2$ in the region is

Which statement$(s)$ among the following are incorrect:
$(i)$ $A$ negative test charge experiences a force opposite to the direction of the field.
$(ii)$ The tangent drawn to a line of force represents the direction of electric field.
$(iii)$ The electric field lines never intersect.
$(iv)$ The electric field lines form a closed loop.

$A$ positive charge $Q$ is situated at the centre of a cube. The electric flux through any face of the cube is (in $SI$ units)