Two point charges of $40 \ \mu C$ and $-20 \ \mu C$ are placed at a certain distance. If they are brought into contact and then placed at the same distance,what is the ratio of the electrostatic force in the two cases?

How much work is done in moving a charge $+q$ once around a circle of radius $r$ in the presence of a central charge $+Q$?

$A$ charged cork of mass $m$ suspended by a light string is placed in a uniform electric field of strength $E = (\hat{i} + \hat{j}) \times 10^5 \ NC^{-1}$ as shown in the figure. If in the equilibrium position,the tension in the string is $\frac{2mg}{(1 + \sqrt{3})}$,then the angle $\alpha$ with the vertical is:

$A$ table tennis ball,which has been covered with conducting paint,is suspended by a silk thread so that it hangs between two plates. One plate is earthed,and the other is connected to a high-voltage generator. This ball:

Six charges,three positive and three negative of equal magnitude,are placed at the corners of a regular hexagon such that the electric field at the center $O$ is double the electric field obtained when only a charge of the same magnitude is placed at $R$. What are the charges at $P, Q, R, S, T,$ and $U$ respectively?

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.]