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.]

Six charges,three positive and three negative of equal magnitude,are to be placed at the vertices of a regular hexagon such that the electric field at $O$ is double the electric field when only one positive charge of the same magnitude is placed at $R$. Which of the following arrangements of charges is possible for $P, Q, R, S, T,$ and $U$ respectively?

Consider two point charges of equal magnitude and opposite sign separated by a certain distance. The neutral point due to them

Consider a gravity-free container as shown. The system is initially at rest and the electric potential in the region is $V = (y^3 + 2) \text{ J/C}$. A ball of charge $q = -0.5 \text{ C}$ and mass $m = 2 \text{ kg}$ is released from rest from the base $(y=0)$. It starts to move up due to the electric field and collides with the shaded top face $(y=2 \text{ m})$ as shown. If its speed just after the collision is $1.5 \text{ m/s}$ and the time for which the ball is in contact with the shaded face is $0.1 \text{ s}$, find the external force required to hold the container fixed in its position during the collision, assuming the ball exerts a constant force on the wall during the entire span of the collision. (in $\text{ N}$)

Electric charges $Q$ are placed on the $x$-axis at $x = 1, 2, 4, 8, \dots \text{meters}$ respectively. What are the electric field and electric potential at $x = 0$?

In free space,a particle $A$ of charge $1\,\mu C$ is held fixed at a point $P.$ Another particle $B$ of the same charge and mass $4\,\mu g$ is kept at a distance of $1\,mm$ from $P$. If $B$ is released,then its velocity at a distance of $9\,mm$ from $P$ is [ Take $\frac{1}{4\pi \varepsilon_0} = 9 \times 10^9\,N m^2 C^{-2}$ ]