A charge $q$ is placed in the middle of a line joining the two equal and like point charge $Q$. This charge $q$ will remain in equilibrium for which value of $q$ is

Two free point charges $+q$ and $+4q$ are a distance $R$ apart. $A$ third charge is so  placed that the entire system is in equilibrium. Then the third charge is :-

Two spherical conductors $B$ and $C$ having equal radii and carrying equal charges in them repel each other with a force $F$ when kept apart at some distance. A third spherical conductor having same radius as that of $B$ but uncharged is brought in contact with $B$, then brought in contact with $C$ and finally removed away from both. The new force of repulsion between $B$ and $C$ is

Charges $4Q$, $q$ and $Q$ and placed along $x$-axis at positions $x = 0,x = l/2$ and $x = l$, respectively. Find the value of $q$ so that force on charge $Q$ is zero

Two small spheres each of mass $10 \,mg$ are suspended from a point by threads $0.5 \,m$ long. They are equally charged and repel each other to a distance of $0.20 \,m$. The charge on each of the sphere is $\frac{ a }{21} \times 10^{-8} \, C$. The value of $a$ will be ...... .

$\left[\right.$ Given $\left.g=10 \,ms ^{-2}\right]$

There are two charges $+1$ microcoulombs and $+5$ microcoulombs. The ratio of the forces acting on them will be