There is a uniform spherically symmetric surface charge density at a distance $R_0$ from the origin. The charge distribution is initially at rest and starts expanding because of mutual repulsion. The figure that represents best the speed $V(R(t))$ of the distribution as a function of its instantaneous radius $R(t)$ is

The surface of a planet is found to be uniformly charged. When a particle of mass $m$ and no charge is thrown at an angle from the surface of the planet,it has a parabolic trajectory as in projectile motion with horizontal range $L$. $A$ particle of mass $m$ and charge $q$,with the same initial conditions,has a range $L/2$. The range of a particle of mass $m$ and charge $2q$,with the same initial conditions,is:

Two point charges $4\,\mu C$ and $-1\,\mu C$ are kept at a distance of $3\ m$ from each other. What is the electric potential at the point where the electric field is zero?

$A$ negative point charge is placed at point $A$ as shown in the figure. The charge is:

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 repulsive force between two point charges is $F$ when they are separated by a distance of $1 \, m$. Now,these point charges are replaced by spheres of radius $25 \, cm$ having the same charges. The distance between their centers is $1 \, m$. The repulsive force in the two cases will decrease according to: