An electron is rotating around an infinite positive linear charge in a circle of radius $0.1 \,m$. If the linear charge density is $1 \,\mu C/m$,then the velocity of the electron in $m/s$ will be ...... $\times 10^7$.

$A$ ball of mass $1 \text{ g}$ having a charge of $20 \mu\text{C}$ is tied to one end of a string of length $0.9 \text{ m}$ and can rotate in a vertical plane in a uniform electric field of $100 \text{ NC}^{-1}$ directed upwards. The minimum horizontal velocity that must be given to the ball at the lowest position so that it completes the vertical circle is (Let $g = 10 \text{ ms}^{-2}$): (in $\text{ ms}^{-1}$)

$A$ proton and an $\alpha$-particle are placed in a uniform electric field. The accelerations produced in them are $a_p$ and $a_\alpha$ respectively. Then $a_p : a_\alpha$ will be . . . . . . .

An oil drop having a mass $4.8 \times 10^{-13} \,kg$ and charge $2.4 \times 10^{-18} \,C$ stands still between two charged horizontal plates separated by a distance of $1 \,cm$. If now the polarity of the plates is changed,the instantaneous acceleration of the drop is: $(g = 10 \,m/s^2)$ (in $\,m/s^2$)

An electron falls through a small distance in a uniform electric field of magnitude $2 \times 10^4 \ N C^{-1}$. The direction of the field is reversed keeping the magnitude unchanged and a proton falls through the same distance. The time of fall will be

The potential difference between two metal plates is $800 \, V$ and they are separated by a horizontal distance of $0.02 \, m$. $A$ particle of mass $1.96 \times 10^{-15} \, kg$ is held in equilibrium between the plates. If $e$ is the elementary charge,then the charge on the particle is .......