Two insulated charged metallic spheres $P$ and $Q$ of negligible radii have their centres separated by a distance of $60 \,cm$. The mutual force of electrostatic repulsion, if the charge on each is $6 \times 10^{-7} \,C$, is

$A$ 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:

$A$ total charge $Q$ is broken into two parts $Q_1$ and $Q_2$ and they are placed at a distance $R$ from each other. The maximum force of repulsion between them will occur when:

Two identical conducting spheres carry identical charges. If the spheres are set at a certain distance apart,they repel each other with a force $F$. $A$ third conducting sphere identical to the other two,but initially uncharged,is touched to one sphere and then to the other before being removed. The force between the original two spheres is now

$(a)$ 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.