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

Two particles each of mass $m$ and charge $q$ are separated by distance $r_1$ and the system is left free to move at $t = 0$. At time $t$,both the particles are found to be separated by distance $r_2$. The speed of each particle is

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?

Three point charges are placed at the corners of an equilateral triangle of side $L$ as shown in the figure.

Two positively charged particles $X$ and $Y$ are initially far away from each other and at rest. $X$ begins to move towards $Y$ with some initial velocity. The total momentum and energy of the system are $p$ and $E$.

Two tiny spheres carrying charges $1.5 \; \mu C$ and $2.5 \; \mu C$ are located $30 \; cm$ apart. Find the potential and electric field:
$(a)$ at the mid-point of the line joining the two charges,and
$(b)$ at a point $10 \; cm$ from this midpoint in a plane normal to the line and passing through the mid-point.