Two identical balls having like charges $Q_1$ and $Q_2$ are placed at a certain distance $r$ apart and repel each other with a force $F_1$. They are brought into contact and then moved apart to a distance equal to half their initial separation $(r/2)$. The force of repulsion between them increases $4.5$ times in comparison with the initial value. The ratio of the initial charges of the balls is

Two charged identical metal spheres $A$ and $B$ repel each other with a force of $3 \times 10^{-5} \,N$. Another identical uncharged sphere $C$ is touched with sphere $A$ and then it is placed mid-way between $A$ and $B$. Then, the magnitude of net force on $C$ is

$A$ clock dial has point charges $-q, -2q, -3q, \ldots, -12q$ at the positions of the corresponding numbers on the dial respectively. The time at which the hour hand points in the direction of the net electric field at the centre of the dial is (Assume clock hands do not influence the net electric field). (in $:30$)

$A$ cube of side $b$ has a charge $q$ at each of its vertices. The electric field due to this charge distribution at the centre of this cube will be

Two metal plates $(A, B)$ are kept horizontally with a separation of $(\frac{12}{\pi}) \text{ cm}$,with plate $A$ on the top. An atomizer jet sprays oil (density $1.5 \text{ g/cm}^3$) droplets of radius $1 \text{ mm}$ horizontally. All oil droplets carry a charge of $5 \text{ nC}$. The potentials $V_A$ and $V_B$ are required on plates $A$ and $B$ respectively in order to ensure the droplets do not descend. The values of $V_A$ and $V_B$ are . . . . . . . (Neglect the air resistance to the droplets and take $g = 10 \text{ m/s}^2$)

Which of the following is true for the figure showing electric lines of force? ($E$ is electrical field,$V$ is potential)