An infinitely long thin wire,having a uniform charge density per unit length of $5 \text{ nC/m}$,is passing through a spherical shell of radius $1 \text{ m}$,as shown in the figure. $A$ $10 \text{ nC}$ charge is distributed uniformly over the spherical shell. If the configuration of the charges remains static,the magnitude of the potential difference between points $P$ and $R$,in Volt,is. . . .
[Given: In $SI$ units $\frac{1}{4 \pi \epsilon_0}=9 \times 10^9, \ln 2=0.7$. Ignore the area pierced by the wire.]

The diagrams depict four different charge distributions. All the charged particles are at the same distance $r$ from the origin $(i.e., OA = OB = OC = OD = r)$. $F_1, F_2, F_3,$ and $F_4$ are the magnitudes of the electrostatic force experienced by a point charge $q_0$ kept at the origin in Figure-$1$,Figure-$2$,Figure-$3$,and Figure-$4$ respectively. Choose the correct statement.

The figure represents a crystal unit of cesium chloride, $CsCl$. The cesium atoms, represented by open circles, are situated at the corners of a cube of side $0.40 \, nm$, whereas a $Cl$ atom is situated at the centre of the cube. The $Cs$ atoms are deficient in one electron while the $Cl$ atom carries an excess electron.
$(i)$ What is the net electric field on the $Cl$ atom due to eight $Cs$ atoms?
$(ii)$ Suppose that the $Cs$ atom at the corner $A$ is missing. What is the net force now on the $Cl$ atom due to the seven remaining $Cs$ atoms?

Find the force experienced by the semicircular rod charged with a charge $q$,placed as shown in the figure. The radius of the wire is $R$ and the line of charge with linear charge density $\lambda$ is passing through its center and is perpendicular to the plane of the wire.

Four equal positive charges are fixed at the vertices of a square of side $L$. The $Z$-axis is perpendicular to the plane of the square. The point $z = 0$ is the point where the diagonals of the square intersect. Find the plot of the electric field $E$ due to the four charges as one moves along the $Z$-axis.

Two charged particles,each of mass $3 \ g$ and charge $0.2 \ \mu C$,stay in (vacuum) equilibrium on a horizontal surface with a separation of $20 \ cm$. The coefficient of friction is $\left[\frac{1}{4 \pi \epsilon_0}=9 \times 10^9 \ Nm^2 C^{-2}\right]$ and $\left(g=10 \ ms^{-2}\right)$.