Two parallel infinite line charges with linear charge densities $+\lambda\; C/m$ and $-\lambda\; C/m$ are placed at a distance of $2R$ in free space. What is the electric field mid-way between the two line charges?

What will be the total electric flux through the faces of a cube of side length $a$ if a charge $q$ is placed at:
$(a)$ $A$: a corner of the cube.
$(b)$ $B$: the midpoint of an edge of the cube.

In the figure,a very large plane sheet of positive charge is shown. $P_{1}$ and $P_{2}$ are two points at distances $l$ and $2l$ from the charge distribution. If $\sigma$ is the surface charge density,then the magnitude of electric fields $E_{1}$ and $E_{2}$ at $P_{1}$ and $P_{2}$ respectively are:

Electric field due to an infinite,straight,uniformly charged wire varies with distance $r$ as:

$A$ cubical volume is bounded by the surfaces $x = 0, x = a, y = 0, y = a, z = 0, z = a$. The electric field in the region is given by $\overrightarrow{E} = E_0 x \hat{i}$,where $E_0 = 4 \times 10^4 \text{ N C}^{-1} \text{m}^{-1}$. If $a = 2 \text{ cm}$,the charge contained in the cubical volume is $Q \times 10^{-14} \text{ C}$. The value of $Q$ is $...........$ (Take $\varepsilon_0 = 9 \times 10^{-12} \text{ C}^2 \text{ N}^{-1} \text{m}^{-2}$)

$A$ spherically symmetric charge distribution is characterized by a charge density $\rho(r) = \rho_0 \left( \frac{5}{4} - \frac{r}{R} \right)$ for $r \le R$ and $\rho(r) = 0$ for $r > R$,where $r$ is the distance from the origin. The electric field at a distance $r$ from the origin $(r < R)$ is given by: