$A$ charge $q$ is placed at one corner of a cube. The electric flux through any of the three faces adjacent to the charge is zero. The flux through any one of the other three faces is

This question has Statement-$1$ and Statement-$2$. Of the four choices given after the statements,choose the one that best describes the two statements.
An insulating solid sphere of radius $R$ has a uniformly positive charge density $\rho$. As a result of this uniform charge distribution,there is a finite value of electric potential at the centre of the sphere,at the surface of the sphere,and also at a point outside the sphere. The electric potential at infinity is zero.
Statement-$1$: When a charge $q$ is taken from the centre to the surface of the sphere,its potential energy changes by $\frac{q \rho R^2}{6 \epsilon_0}$.
Statement-$2$: The electric field at a distance $r (r < R)$ from the centre of the sphere is $\frac{\rho r}{3 \epsilon_0}$.

The electric field intensity at $P$ and $Q$,in the shown arrangement,are in the ratio:

$A$ small bob of mass $100 \ mg$ and charge $+10 \ \mu C$ is connected to an insulating string of length $1 \ m$. It is brought near to an infinitely long nonconducting sheet of charge density $\sigma$ as shown in the figure. If the string subtends an angle of $45^{\circ}$ with the sheet at equilibrium,the charge density of the sheet will be (Given,$\varepsilon_0 = 8.85 \times 10^{-12} \ F/m$ and acceleration due to gravity,$g = 10 \ m/s^2$): (in $nC/m^2$)

$A$ parallel plate capacitor consists of two metal plates. One plate is given a charge of $+q$,while the other is connected to the ground. Points $P, P_1$,and $P_2$ are taken as shown in the figure. At which point is the electric field $NOT$ zero?

The electric field at a distance $r$ from the centre in the space between two concentric metallic spherical shells of radii $r_1$ and $r_2$ carrying charges $Q_1$ and $Q_2$ respectively is $(r_1 < r < r_2)$.