An electric field due to a positively charged long straight wire at a distance $r$ from it is proportional to $r^{-1}$ in magnitude. Two electrons are orbiting such a long straight wire in circular orbits of radii $1 A$ and $2 A$. The ratio of their respective time periods is

Three identical charged balls each of charge $2 \,C$ are suspended from a common point $P$ by silk threads of $2 \,m$ each (as shown in figure). They form an equilateral triangle of side $1 \,m$.

The ratio of net force on a charged ball to the force between any two charged balls will be ...........

Two identical metallic spheres $A$ and $B$ when placed at certain distance in air repel each other with a force of $F$. Another identical uncharged sphere $C$ is first placed in contact with $A$ and then in contact with $B$ and finally placed at midpoint between spheres $A$ and $B$. The force experienced by sphere $C$ will be.

An infinite number of point charges, each carrying $1 \,\mu C$ charge, are placed along the y-axis at $y=1\, m , 2\, m , 4 \,m , 8\, m \ldots \ldots \ldots \ldots \ldots$

The total force on a $1 \,C$ point charge, placed at the origin, is $x \times 10^{3}\, N$. The value of $x$, to the nearest integer, is .........

[Take $\left.\frac{1}{4 \pi \epsilon_{0}}=9 \times 10^{9} \,Nm ^{2} / C ^{2}\right]$

If two charges of $1$ coulomb each are placed $1 \,km$ apart, then the force between them will be ........... $N$