Two positive point charges of $12\,\mu C$ and $8\,\mu C$ are $10\,cm$ apart. The work done in bringing them $4\, cm$ closer is

$(a)$ In a quark model of elementary particles, a neutron is made of one up quarks [ 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 electrostatic potential energy of neutron and compare it with its mass $939$ $Me\,V$. $(b)$ Repeat above exercise for a proton which is made of two up and one down quark.

$(a)$ Determine the electrostatic potential energy of a system consisting of two charges $7 \;\mu C$ and $-2\; \mu C$ (and with no external field) placed at $(-9 \;cm , 0,0)$ and $(9\; cm , 0,0)$ respectively.

$(b)$ How much work is required to separate the two charges infinitely away from each other?

$(c)$ Suppose that the same system of charges is now placed in an external electric field $E=A\left(1 / r^{2}\right) ; A=9 \times 10^{5} \;C m ^{-2} .$ What would the electrostatic energy of the configuration be?

A block of mass $m$ containing a net negative charge $-q$ is placed on a frictionless  horizontal table and is connected to a wall through an unstretched spring of spring  constant $k$ as shown. If horizontal electric field $E$ parallel to the spring is switched on,  then the maximum compression of the spring is :-

$n$ the rectangle, shown below, the two corners have charges ${q_1} = – 5\,\mu C$ and ${q_2} = + 2.0\,\mu C$. The work done in moving a charge $ + 3.0\,\mu C$ from $B$ to $A$ is………$J$ $(1/4\pi {\varepsilon _0} = {10^{10}}\,N{\rm{ – }}{m^2}/{C^2})$