The electric field $\vec{E} = E_0 y \hat{j}$ acts in a space where a cylinder of radius $r$ and length $l$ is placed with its axis parallel to the $y$-axis. The charge inside the volume of the cylinder is:

Charges $Q, 2Q$ and $4Q$ are uniformly distributed in three dielectric solid spheres $1, 2$ and $3$ of radii $R/2, R$ and $2R$ respectively,as shown in the figure. If magnitudes of the electric fields at point $P$ at a distance $R$ from the centre of spheres $1, 2$ and $3$ are $E_1, E_2$ and $E_3$ respectively,then:

$X$ and $Y$ are large,parallel conducting plates close to each other. Each face has an area $A$. $X$ is given a charge $Q$. $Y$ is without any charge. Points $A, B$,and $C$ are as shown in the figure.

Consider a solid insulating sphere of radius $R$ with charge density varying as $\rho = \rho_0 r^2$,where $\rho_0$ is a constant and $r$ is measured from the centre. Consider two points $A$ and $B$ at distances $x$ and $y$ respectively $(x < R, y > R)$ from the centre. If the magnitudes of the electric fields at points $A$ and $B$ are equal,then:

$A$ thin metallic spherical shell of radius $r$ contains a charge $Q$ on its surface. $A$ point charge $q_1$ is placed at the centre of the shell and another charge $q_2$ is placed outside the shell at a distance $x$ from the centre. Then, the forces on charges $q_1$ and $q_2$ respectively are

$A$ spherically symmetric charge distribution is considered with charge density varying as
$\rho(r)=\begin{cases} \rho_{0}\left(\frac{3}{4}-\frac{r}{R}\right) & \text{for } r \leq R \\ 0 & \text{for } r>R \end{cases}$
Where,$r (r < R)$ is the distance from the centre $O$ (as shown in figure). The electric field at point $P$ will be.