$A$ cube of side $a$ is placed in an electric field $\vec{E} = E_0 x \hat{i}$. What is the total charge enclosed by the cube?

Two large parallel plates have uniform surface charge densities $+\sigma$ and $-\sigma$. The electric field between the plates is:

$A$ spherical shell with an inner radius $a$ and an outer radius $b$ is made of conducting material. $A$ point charge $+Q$ is placed at the centre of the spherical shell and a total charge $-q$ is placed on the shell. Charge $-q$ is distributed on the surfaces as:

$A$ 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:

$A$ spherical portion has been removed from a solid sphere having a charge distributed uniformly in its volume as shown in the figure. The electric field inside the emptied space is

An infinite line of charge with uniform line charge density of $\lambda = 1 \ C \ m^{-1}$ is placed along the $y$-axis. $A$ point charge $q = 1 \ C$ is placed on the $x$-axis at a distance of $d = 3 \ m$ from the origin. At what distance $r$ from the origin on the $x$-axis,between the origin and the point charge,is the total electric field zero (in $m$)?