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

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.

$5$ charges each of magnitude $10^{-5} \,C$ and mass $1 \,kg$ are placed (fixed) symmetrically about a movable central charge of magnitude $5 \times 10^{-5} \,C$ and mass $0.5 \,kg$ as shown in the figure given below. The charge at $P_1$ is removed. The acceleration of the central charge is [Given, $\left.O P_1=O P_2=O P_3=O P_4=O P_5=1 m , \frac{1}{4 \pi \varepsilon_0}=9 \times 10^9\right]$

Three point charges are placed at the corners of an equilateral triangle. Assuming only electrostatic forces are acting

The distance between charges $5 \times {10^{ - 11}}\,C$ and $ - 2.7 \times {10^{ - 11}}\,C$ is $0.2\, m$. The distance at which a third charge should be placed in order that it will not experience any force along the line joining the two charges is......$m$

A charged particle having some mass is resting in equilibrium at a height $H$ above the centre of a uniformly charged non-conducting horizontal ring of radius $R$. The force of gravity acts downwards. The equilibrium of the particle will be stable $R$