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 placed at the centre of the line joining two equal charges $Q$. The system of the three charges will be in equilibrium if $q$ is equal to:

Charges $q, 2q, 3q,$ and $4q$ are placed at the corners of a square as shown in the figure. $A$ charge $q_0$ is placed at its center. Find the net force on the charge $q_0$.

$(a)$ 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.

Four charges equal to $-Q$ are placed at the four corners of a square and a charge $q$ is at its centre. If the system is in equilibrium,the value of $q$ is

Two identical conducting spheres with negligible volume have $2.1 \, nC$ and $-0.1 \, nC$ charges,respectively. They are brought into contact and then separated by a distance of $0.5 \, m$. The electrostatic force acting between the spheres is $.......... \times 10^{-9} \, N$. [Given: $\frac{1}{4 \pi \varepsilon_{0}} = 9 \times 10^{9} \, N \cdot m^{2}/C^{2}$]