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 identical spheres are charged with equal charges and the force between them is $F$. If $50\%$ of the charge from one sphere is transferred to the other sphere,then the new force will be ........ $F$.

Two charged spheres are suspended by strings of equal length. The strings make an angle of $30^{\circ}$ with each other. When suspended in a liquid of density $0.8 \ g/cm^3$,the angle remains the same. The dielectric constant of the liquid is ........ (The density of the material of the sphere is $1.6 \ g/cm^3$.)

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 $= 1.67 \times 10^{-27} \; kg$):

An infinite number of charges,each of charge $1 \,\mu C$,are placed on the $x$-axis at coordinates $x = 1, 2, 4, 8, ... \infty$. If a charge of $1 \, C$ is kept at the origin,what is the net force acting on the $1 \, C$ charge in Newtons?

$A$ charge $Q$ is divided into two parts $q$ and $Q - q$. If the Coulomb repulsion between them when they are separated by a distance $r$ is to be maximum,the ratio of $\frac{Q}{q}$ should be: