$A$ charged particle is suspended in equilibrium in a uniform vertical electric field of intensity $20,000\, V/m$. If the mass of the particle is $9.6 \times 10^{-16}\, kg$,the charge on it and the excess number of electrons on the particle are respectively $(g = 10\, m/s^2)$.

An electron moving with a speed of $5 \times 10^6 \, m/s$ is shot parallel to an electric field of intensity $1 \times 10^3 \, N/C$. The field causes retardation of the electron's motion. Evaluate the distance traveled by the electron before coming to rest for an instant (mass of $e = 9 \times 10^{-31} \, kg$,charge $q = 1.6 \times 10^{-19} \, C$).

$A$ $2 \ g$ object,located in a region of uniform electric field $E = (300 \ NC^{-1}) \hat{i}$,carries a charge $Q$. The object is released from rest at $x = 0$ and has a kinetic energy of $0.12 \ J$ at $x = 0.5 \ m$. Then,$Q$ is: (in $\mu C$)

The figure shows the paths of three charged particles in a uniform electric field. Which particle has the highest charge-to-mass ratio?

$A$ charged cork ball having mass $1 \text{ g}$ and charge $q$ is suspended on a light string in a uniform electric field as shown in the figure. The ball is in equilibrium at $\theta=37^{\circ}$,when the value of the electric field is $E=(3 \hat{i}+5 \hat{j}) \times 10^5 \text{ NC}^{-1}$. (Assume $T$ as tension in the string.) Which of the following options are correct? (Given,$\sin 37^{\circ}=0.60$ and $g=10 \text{ ms}^{-2}$)

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 $1 \mathring{A}$ and $2 \mathring{A}$. The ratio of their respective time periods is