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 electrostatic force on a small sphere of charge $0.4 \;\mu\, C$ due to another small sphere of charge $-0.8 \;\mu \,C$ in air is $0.2\; N .$

$(a)$ What is the distance between the two spheres?

$(b)$ What is the force on the second sphere due to the first?

A particle of charge $-q$ and mass $m$ moves in a circle of radius $r$ around an infinitely long line charge of linear density $+\lambda$. Then time period will be given as

(Consider $k$ as Coulomb's constant)

The law, governing the force between electric charges is known as

Two point charges $A$ and $B$, having charges $+Q$ and $- Q$ respectively, are placed at certain distance apart and force acting between them is $\mathrm{F}$. If $25 \%$ charge of $A$ is transferred to $B$, then force between the charges becomes

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