Four electric charges $+Q, -Q, +Q$,and $-Q$ are placed at the four corners of a square. What are the electric field $(E)$ and electric potential $(V)$ at the center of the square?

In the given square $ABCD$,charges $q$,$2q$,$3q$,and $4q$ are placed at corners $A$,$B$,$C$,and $D$ respectively. What is the direction of the net electric field at the center $O$?

An ellipsoidal cavity is carved within a perfect conductor. $A$ positive charge $q$ is placed at the centre of the cavity. The points $A$ and $B$ are on the cavity surface as shown in the figure. Then

Two charged particles of mass $1 \ g$ each are placed $1 \ m$ apart. If each of these possesses $1 \ fC$ (femto coulomb) of charge, then the dominant force of interaction between them is:

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

Two small conducting spheres of equal radius have charges of $10\ \mu C$ and $-20\ \mu C$ respectively and are placed at a distance $R$ from each other,experiencing a force $F_1$. If they are brought in contact and then separated to the same distance,the new force between them is $F_2$. Find the ratio $F_1 : F_2$.