Two point charges $+e$ and $+4e$ are kept at a distance $d$ units apart. $A$ third point charge $+q$ is placed between the two charges at a distance $x$ units from charge $+e$ so as to be in equilibrium. The value of $x$ is:

Two similar spheres having $+q$ and $-q$ charge are kept at a certain distance $r$. $A$ force $F$ acts between them. If another similar sphere having $+q$ charge is kept in the middle of the two spheres, then it experiences a force in magnitude and direction as:

Three charges each of magnitude $q$ are placed at the corners of an equilateral triangle. The electrostatic force on the charge $Q$ placed at the center is (each side of the triangle is $L$):

Two spheres of radii $3 \ cm$ and $1 \ cm$ are placed at a distance of $10 \ cm$ from each other in a vacuum. If each sphere is charged to a potential of $10 \ V$,the force of repulsion between them is:

$A$ certain charge $2Q$ is divided at first into two parts $q_{1}$ and $q_{2}$. Later,the charges are placed at a certain distance. If the force of interaction between the two charges is maximum,then find the value of $\frac{Q}{q_{1}}$.

The ratio of Coulomb's electrostatic force to the gravitational force between an electron and a proton separated by some distance is $2.4 \times 10^{39}$. The ratio of the proportionality constant $K = \frac{1}{4 \pi \varepsilon_0}$ to the gravitational constant $G$ is nearly (Given that the charge of the proton and electron each $= 1.6 \times 10^{-19} \; C$,the mass of the electron $= 9.11 \times 10^{-31} \; kg$,the mass of the proton $= 1.67 \times 10^{-27} \; kg$):