Three charges $4q$,$Q$,and $q$ are placed in a straight line at positions $0$,$l/2$,and $l$ respectively. The resultant force on $q$ will be zero if $Q = $

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

Charges $q, 2q, 3q,$ and $4q$ are placed at the corners of a square as shown in the figure. $A$ charge $q_0$ is placed at its center. Find the net force on the charge $q_0$.

Three charges $q, Q$ and $+4q$ are placed in a straight line of length $d$ at positions $0, d/3$ and $2d/3$ respectively. In order to make the net force on $q$ be zero, the value of $Q$ should be

Two identical charged conducting spheres $A$ and $B$ have their centres separated by a certain distance. Charge on each sphere is $q$ and the force of repulsion between them is $F$. $A$ third identical uncharged conducting sphere $C$ is brought in contact with sphere $A$ first and then with $B$ and finally removed from both. The new force of repulsion between spheres $A$ and $B$ (radii of $A$ and $B$ are negligible compared to the distance of separation so that for calculating force between them they can be considered as point charges) is best given as:

$A$ and $B$ are two identical blocks made of a conducting material. These are placed on a horizontal frictionless table and connected by a light conducting spring of force constant $K$. The unstretched length of the spring is $L_0$. $A$ charge $Q/2$ is given to each block. Consequently,the spring stretches to an equilibrium length $L$. The value of $Q$ is