Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of $30^o$ with each other. When suspended in a liquid of density $1 \, g \, cm^{-3}$,the angle remains the same. If the density of the material of the sphere is $4/3 \, g \, cm^{-3}$,the dielectric constant of the liquid is:

Two protons are separated by a distance of $10^{-10} \ m$. If they are released,what will be their total kinetic energy at an infinite distance?

$A$ total charge $q$ is divided into $q_1$ and $q_2$,which are placed at two vertices of an equilateral triangle of side $a$. The magnitude of the electric field $E$ at the third vertex of the triangle is to be depicted schematically as a function of $x = q_1 / q$. Choose the correct figure.

Two identical point charges are placed at a separation of $l$. $P$ is a point on the line joining the charges,at a distance $x$ from any one charge. The field at $P$ is $E$. $E$ is plotted against $x$ for values of $x$ from close to zero to slightly less than $l$. Which of the following best represents the resulting curve?

The electric field $E$ is measured at a point $P(0, 0, d)$ generated due to various charge distributions and the dependence of $E$ on $d$ is found to be different for different charge distributions. List-$I$ contains different relations between $E$ and $d$. List-$II$ describes different electric charge distributions,along with their locations. Match the functions in List-$I$ with the related charge distributions in List-$II$.

List-$I$	List-$II$
$P$. $E$ is independent of $d$	$1$. $A$ point charge $Q$ at the origin
$Q$. $E \propto \frac{1}{d}$	$2$. $A$ small dipole with point charges $Q$ at $(0, 0, l)$ and $-Q$ at $(0, 0, -l)$. Take $2l \ll d$.
$R$. $E \propto \frac{1}{d^2}$	$3$. An infinite line charge coincident with the $x$-axis,with uniform linear charge density $\lambda$
$S$. $E \propto \frac{1}{d^3}$	$4$. Two infinite wires carrying uniform linear charge density parallel to the $x$-axis. The one along $(y=0, z=l)$ has a charge density $+\lambda$ and the one along $(y=0, z=-l)$ has a charge density $-\lambda$. Take $2l \ll d$
	$5$. Infinite plane with uniform surface charge density

$A$ positively charged thin metal ring of radius $R$ is fixed in the $xy$-plane with its centre at the origin $O$. $A$ negatively charged particle $P$ is released from rest at the point $(0, 0, z_0)$,where $z_0 > 0$. Then the motion of $P$ is: