Which of the following statement(s) correct ? 

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

The figure below depict two situations in which two infinitely long static line charges of constant positive line charge density $\lambda$ are kept parallel to each other. In their resulting electric field, point charges $q$ and $-q$ are kept in equilibrium between them. The point charges are confined to move in the $x$-direction only. If they are given a small displacement about their equilibrium positions, then the correct statement (s) is (are)

Consider a uniform spherical charge distribution of radius $R_1$ centered at the origin $O$. In this distribution, a spherical cavity of radius, centered at $P$ with distance $OP=a=R_1-R_2$ (see figure) is made. If the electric field inside the cavity at position $\overrightarrow{r}$ is $\overrightarrow{E}\left(\overrightarrow{r}\right)$, then the correct statement is / are:

A cubical region of side a has its centre at the origin. It encloses three fixed point charges, $-q$ at $\left(0, -\frac{a}{4}, 0\right), +3q$ at $\left(0, 0, 0\right), -q$ at $\left(0, +a/4, 0\right)$. Choose the correct option(s).

Two nonconducting solid spheres of radii $R$ and $2R$ having uniform volume charge densities ${\rho }_1$ and ${\rho }_2$, respectively, touch each other. The net electric field at a distance $2R$ from the centre of the smaller sphere, along the line joining the centre of the spheres, is zero. The ratio $\frac{{\rho }_1}{{\rho }_2}$ can be:

Two nonconducting spheres of radii $R_1$ and $R_2$ and carrying uniform volume charge densities $+\rho$ and $-\rho$, respectively, are placed such that they partially overlap, as shown in the figure. At all points in the overlapping region, 

A point charge $+Q$ is placed just outside an imaginary hemispherical surface of radius $R$ as shown in the figure. Which of the following statements is/are correct?