Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle $\theta$ with each other. When suspended in water,the angle remains the same. If the density of the material of the sphere is $1.5 \ g/cc$,the dielectric constant of water will be (Take density of water $= 1 \ g/cc$)

$(a)$ In a quark model of elementary particles,a neutron is made of one up quark [ charge $\frac{2}{3}e$ ] and two down quarks [ charges $-\frac{1}{3}e$ ]. Assume that they have a triangle configuration with side length of the order of ${10^{ - 15}} \ m$. Calculate the electrostatic potential energy of the neutron and compare it with its mass $939 \ MeV$. $(b)$ Repeat the above exercise for a proton which is made of two up and one down quark.

Two pith balls, each carrying charge $+q$, are hung from a hook by two strings of length $L$. It is found that when each charge is tripled, the angle between the strings doubles. What was the initial angle between the strings (in $^{\circ}$)?

If two charges $q_1$ and $q_2$ are separated by a distance '$d$' and placed in a medium of dielectric constant $K$,what will be the equivalent distance between the charges in air for the same electrostatic force?

$A$ charge $Q$ is divided into two parts $q$ and $Q-q$ and separated by a distance $R$. The force of repulsion between them will be maximum when:

Two balls with charges $+7 \ \mu C$ and $-5 \ \mu C$ attract each other with a force $F$. If $-2 \ \mu C$ charge is added to both,what will be the force between them?