When two identical point charges are placed at a distance of $5 \, cm$, they experience a repulsive force of $0.144 \, N$. The value of each charge in microcoulombs $(\mu C)$ is:

An oil drop of $12$ excess electrons is held stationary under a constant electric field of $2.55 \times 10^{4} \; N \, C^{-1}$ (Millikan's oil drop experiment). The density of the oil is $1.26 \; g \, cm^{-3}$. Estimate the radius of the drop. $(g = 9.81 \; m \, s^{-2}; e = 1.60 \times 10^{-19} \; C)$

$(a)$ 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.

Three charges $4q, Q$ and $q$ are in a straight line along the $x$-axis at the positions $x=0 \ m$,$x=\frac{1}{2} \ m$,and $x=1 \ m$ respectively. The resultant force on $q$ will be zero if $Q$ is equal to:

$A$ charged metallic sphere $A$ is suspended by a nylon thread. Another charged metallic sphere $B$ held by an insulating handle is brought close to $A$ such that the distance between their centres is $10 \, cm$,as shown in Figure $(a)$. The resulting repulsion of $A$ is noted (for example,by shining a beam of light and measuring the deflection of its shadow on a screen). Spheres $A$ and $B$ are touched by uncharged spheres $C$ and $D$ respectively,as shown in Figure $(b)$. $C$ and $D$ are then removed and $B$ is brought closer to $A$ to a distance of $5.0 \, cm$ between their centres,as shown in Figure $(c)$. What is the expected repulsion of $A$ on the basis of Coulomb's law? Spheres $A$ and $C$ and spheres $B$ and $D$ have identical sizes. Ignore the sizes of $A$ and $B$ in comparison to the separation between their centres.

In a right-angled triangle $ABC$,$AB = 3 \ cm$,$BC = 4 \ cm$,and $\angle ABC = \frac{\pi}{2}$. Charges of $+15 \ e.s.u.$,$+12 \ e.s.u.$,and $-20 \ e.s.u.$ are placed at $A$,$B$,and $C$ respectively. What is the net force on the charge at $B$ in $dynes$?