$A$ cube is placed inside an electric field,$\overrightarrow{E} = 150 y^2 \hat{j}$. The side of the cube is $0.5 \, m$ and it is placed in the field as shown in the figure. The charge inside the cube is $..... \times 10^{-11} \, C$.

Consider a uniform spherical volume charge distribution of radius $R$. Which of the following graphs correctly represents the magnitude of the electric field $E$ at a distance $r$ from the centre of the sphere?

For a uniformly charged plane sheet, the variation of electric field $(E)$ with distance $(d)$ is correctly shown graphically in graph:

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:

$A$ spherically symmetric charge distribution is characterised by a charge density having the following variations:
$\rho (r) = \rho_0 \left( 1 - \frac{r}{R} \right)$ for $r < R$
$\rho (r) = 0$ for $r \ge R$
Where $r$ is the distance from the centre of the charge distribution and $\rho_0$ is a constant. The electric field at an internal point $(r < R)$ is:

Three infinitely long charged sheets are placed as shown in the figure. The electric force acting on a charge $-q$ placed at the point $P$ is ($\sigma=$ surface charge density,$\varepsilon_0=$ permittivity of free space).