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

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 $= 6.37 \times 10^{6} \; m$.)

Two identical charged spheres suspended from a common point by two massless strings of lengths $l$ are initially at a distance $d$ $(d << l)$ apart because of their mutual repulsion. The charges begin to leak from both the spheres at a constant rate. As a result,the spheres approach each other with a velocity $v$. Then $v$ varies as a function of the distance $x$ between the spheres,as:

This question contains Statement-$1$ and Statement-$2$. Of the four choices given after the statements,choose the one that best describes the two statements.
Statement-$1$ : For a charged particle moving from point $P$ to point $Q$,the net work done by an electrostatic field on the particle is independent of the path connecting point $P$ to point $Q$.
Statement-$2$ : The net work done by a conservative force on an object moving along a closed loop is zero.

Three point charges $q_1, q_2, q_3$ are placed at the vertices of a triangle. If the forces on $q_1$ and $q_2$ are $(2\hat{i} - \hat{j}) \, N$ and $(\hat{i} + 3\hat{j}) \, N$,respectively,then what will be the force on $q_3$?

Two identical charged spheres are suspended from a common point by two massless strings of length $l$. Initially,they are at a distance $d$ $(d << l)$ due to mutual repulsion. The charge begins to leak from both spheres at a constant rate. As a result,the spheres approach each other with a velocity $v$. Then,the velocity $v$ as a function of the distance $x$ between them is: