Point charges $ + 4q,\, - q$ and $ + 4q$ are kept on the $x - $axis at points $x = 0,\,x = a$ and $x = 2a$ respectively, then

A charge of $4\,\mu C$ is to be divided into two. The distance between the two divided charges is constant. The magnitude of the divided charges so that the force between them is maximum, will be.

Coulomb's law for electrostatic force between two point charges and Newton's law for gravitational force between two stationary point masses, both have inverse-square dependence on the distance between the charges and masses respectively.

$(a)$ Compare the strength of these forces by determining the ratio of their magnitudes $(i)$ for an electron and a proton and $(ii)$ for two protons.

$(b)$ Estimate the accelerations of electron and proton due to the electrical force of their mutual attraction when they are $1  \mathring A \left( { = {{10}^{ - 10}}m} \right)$ apart? $\left(m_{p}=1.67 \times 10^{-27} \,kg , m_{e}=9.11 \times 10^{-31}\, kg \right)$

A $10\,\mu C$ charge is divided into two parts and placed at $1\,cm$ distance so that the repulsive force between them is maximum. The charges of the two parts are :

Force between two point charges $q_1$ and $q_2$ placed in vacuum at ' $r$ ' $\mathrm{cm}$ apart is $F$. Force between them when placed in a medium having dielectric $\mathrm{K}=5$ at $\mathrm{r} / 5$ $\mathrm{cm}$ apart will be:

Two equal positive point charges are separated by a distance $2 a$. The distance of a point from the centre of the line joining two charges on the equatorial line (perpendicular bisector) at which force experienced by a test charge $q_0$ becomes maximum is $\frac{a}{\sqrt{x}}$. The value of $x$ is $................$