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

Two point charges $Q$ each are placed at a distance $d$ apart. $A$ third point charge $q$ is placed at a distance $x$ from the mid-point on the perpendicular bisector. The value of $x$ at which charge $q$ will experience the maximum Coulomb force is ...............

An electron is moving around the nucleus of a hydrogen atom in a circular orbit of radius $r$. The Coulomb force $\overrightarrow{F}$ between the two is (where $K = \frac{1}{4\pi\varepsilon_0}$):

Two identical non-conducting solid spheres of same mass and charge are suspended in air from a common point by two non-conducting,massless strings of same length. At equilibrium,the angle between the strings is $\alpha$. The spheres are now immersed in a dielectric liquid of density $\rho_l = 800 \ kg \ m^{-3}$ and dielectric constant $K = 21$. If the angle between the strings remains the same after the immersion,then
$(A)$ electric force between the spheres remains unchanged
$(B)$ electric force between the spheres reduces
$(C)$ mass density of the spheres is $840 \ kg \ m^{-3}$
$(D)$ the tension in the strings holding the spheres remains unchanged

How did Coulomb determine the law of electric force between two point charges?

Two particles of equal mass $m$ and equal charge $q$ are separated by a distance of $16 \text{ cm}$. They do not experience any net force. The value of $\frac{q}{m}$ is . . . . . . (where $G$ is the universal gravitational constant and $\epsilon_0$ is the permittivity of free space).