Dielectric constant of pure water is $81$. Its permittivity will be

A thin metallic wire having cross sectional area of $10^{-4} \mathrm{~m}^2$ is used to make a ring of radius $30 \mathrm{~cm}$. A positive charge of $2 \pi \mathrm{C}$ is uniformly distributed over the ring, while another positive charge of $30$ $\mathrm{pC}$ is kept at the centre of the ring. The tension in the ring is__________ $\mathrm{N}$; provided that the ring does not get deformed (neglect the influence of gravity). (given, $\frac{1}{4 \pi \epsilon_0}=9 \times 10^9 \mathrm{SI}$ units)

The value of electric permittivity of free space is

Two identical tennis balls each having mass $m$ and charge $q$ are suspended from a fixed point by threads of length $l$. What is the equilibrium separation when each thread makes a small angle $\theta$ with the vertical?

$ABC$ is a right angled triangle in which $AB = 3\,cm$ and $BC = 4\,cm$. And  $\angle ABC = \pi /2$. The three charges $ + 15,\; + 12$ and $ - 20\,e.s.u.$ are placed respectively on $A$, $B$ and $C$. The force acting on $B$ is.......$dynes$

Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of $30^{\circ}$ with each other. When suspended in a liquid of density $0.8 \;g\, cm ^{-3}$, the angle remains the same. If density of the material of the sphere is $1.6\; g \,cm ^{-3}$, the dielectric constant of the liquid is