Three point charges are placed at the corners of an equilateral triangle of side $L$ as shown in the figure.

Two small spheres of each charge $q$,mass $m$ and material density $d$ are suspended from a fixed point with the help of inextensible light threads. When the spheres are in air,the angle between the threads is $90^{\circ}$. When the spheres are suspended in a liquid of density $\frac{2}{3} d$,the angle between the threads is $60^{\circ}$. The value of the dielectric constant of the liquid is

Column $II$ corresponds to the graph of magnitude of electric field versus distance from the centre of the charge distribution in Column $I$. Match the items in Column $I$ with the corresponding graphs in Column $II$.

Column-$I$	Column-$II$
$(A)$ Ring along its axis	$(P)$ Graph with a peak at a distance $r > 0$
$(B)$ Uniformly charged solid sphere	$(Q)$ Graph increasing linearly for $r < R$ and decreasing as $1/r^2$ for $r > R$
$(C)$ Uniformly charged spherical shell	$(R)$ Graph with zero field for $r < R$ and decreasing as $1/r^2$ for $r > R$
$(D)$ Combination of charge $+Q$ and $-Q$ at the perpendicular bisector	$(S)$ Graph with a maximum at the center and decreasing as $r$ increases

The energy density $u$ is plotted against the distance $r$ from the centre of a spherical charge distribution on a $log$-$log$ scale. The slope of the obtained straight line is:

Consider a system of three charges $\frac{q}{3}, \frac{q}{3}$ and $-\frac{2q}{3}$ placed at points $A, B$ and $C$,respectively,as shown in the figure. Take $O$ to be the centre of the circle of radius $R$ and angle $\angle CAB = 60^{\circ}$.

Six charges are placed at the corners of a regular hexagon as shown. If an electron is placed at its centre $O$,the force on it will be: