Two identical conducting spheres $A$ and $B$ carry equal charge. They are separated by a distance much larger than their diameter,and the force between them is $F$. $A$ third identical conducting sphere,$C$,is uncharged. Sphere $C$ is first touched to $A$,then to $B$,and then removed. As a result,the force between $A$ and $B$ would be equal to

The earth's surface has a negative surface charge density of $10^{-9} \; C\;m^{-2}$. The potential difference of $400 \; kV$ between the top of the atmosphere and the surface results (due to the low conductivity of the lower atmosphere) in a current of only $1800 \; A$ over the entire globe. If there were no mechanism of sustaining the atmospheric electric field,how much time (roughly) would be required to neutralize the earth's surface (in $; s$)? (This never happens in practice because there is a mechanism to replenish electric charges,namely the continual thunderstorms and lightning in different parts of the globe). (Radius of earth $= 6.37 \times 10^{6} \; m$.)

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.]

Point charges are placed at the vertices of a regular hexagon with center $O$ and side length $L$ as shown in the figure. Given $K = \frac{q}{4\pi \epsilon_0 L^2}$,which of the following statements is correct?

The diagrams depict four different charge distributions. All the charged particles are at the same distance $r$ from the origin $(i.e., OA = OB = OC = OD = r)$. $F_1, F_2, F_3,$ and $F_4$ are the magnitudes of the electrostatic force experienced by a point charge $q_0$ kept at the origin in Figure-$1$,Figure-$2$,Figure-$3$,and Figure-$4$ respectively. Choose the correct statement.

Two equal negative charges $-q$ are placed at points $(0, a)$ and $(0, -a)$ on the $Y$-axis. A positive charge $q$ is released from rest at point $(2a, 0)$. What will be the motion of this charge?