Two concentric spherical surfaces $P_1$ and $P_2$ enclose charges $\frac{Q}{2}$ and $4Q$ as shown in the figure. If $\phi_1$ and $\phi_2$ are the electric fluxes linked with the surfaces $P_1$ and $P_2$ respectively,then:

Why do electric field lines not form closed loops?

An electric field,$\overrightarrow{E} = \frac{2 \hat{i} + 6 \hat{j} + 8 \hat{k}}{\sqrt{6}} \ V/m$,passes through a surface of $4 \ m^2$ area having a unit normal vector $\hat{n} = \left( \frac{2 \hat{i} + \hat{j} + \hat{k}}{\sqrt{6}} \right)$. The electric flux through that surface is:

Consider a region in free space bounded by the surfaces of an imaginary cube having sides of length $a$ as shown in the figure. $A$ charge $+Q$ is placed at the centre $O$ of the cube. $P$ is a point outside the cube such that the line $OP$ perpendicularly intersects the surface $ABCD$ at $R$,and $OR = RP = a/2$. $A$ charge $+Q$ is also placed at point $P$. What is the total electric flux through the five faces of the cube other than $ABCD$?

If charge $q$ is placed on one of the vertex of a cube,then total electric flux passing through the cube is . . . . . . .

Consider a cube of side length '$a$' centered at the origin. It is enclosed by three fixed point charges: $(-q)$ at $(0, -a/4, 0)$,$(+3q)$ at $(0, 0, 0)$,and $(-q)$ at $(0, a/4, 0)$. Choose the correct option.