The electric field in a region is given by $\vec{E}=(2 \hat{i}+4 \hat{j}+6 \hat{k}) \times 10^3 \ N/C$. The flux of the field through a rectangular surface parallel to the $x-z$ plane is $6.0 \ N m^2 C^{-1}$. The area of the surface is . . . . . . $cm^2$.

Draw the electric field lines for a positive point charge.

$A$ charge $Q$ is enclosed by a Gaussian surface of radius $R$. If the radius is doubled,then the outward electric flux will

An infinitely long wire has a uniform linear charge density $\lambda = 2 \ nC/m$. The net flux through a Gaussian cube of side length $a = \sqrt{3} \ cm$, if the wire passes through any two corners of the cube that are maximally displaced from each other, is $x\pi \ Nm^2 C^{-1}$. Find the value of $x$. [Neglect any edge effects and use $\frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \ SI$ units]

$A$ point charge $q$ is placed on the center of the flat circular base of a hemispherical surface as shown in the figure. The net flux of the electric field through the hemispherical surface is closest to:

Select the correct statement$(s)$:
$(1)$ The density of electric field lines is independent of the magnitude of the electric field vector $E$ at a given point.
$(2)$ The density of electric field lines is proportional to the magnitude of the electric field vector $E$ at a given point.
$(3)$ Electric field lines do not exist in reality. They are only a graphical representation of the electric field.
$(4)$ Electric field lines exist in reality.