$A$ block of mass $m$ and charge $q$ is connected to a point $O$ with an inextensible string. This system is on a horizontal table. An electric field $E$ is applied perpendicular to the string and in the plane of the horizontal table. The tension in the string when it becomes parallel to the electric field is

$A$ particle,of mass $10^{-3} \ kg$ and charge $1.0 \ C$,is initially at rest. At time $t = 0$,the particle comes under the influence of an electric field $\vec{E}(t) = E_0 \sin(\omega t) \hat{i}$,where $E_0 = 1.0 \ N \ C^{-1}$ and $\omega = 10^3 \ rad \ s^{-1}$. Consider the effect of only the electrical force on the particle. Then the maximum speed,in $m \ s^{-1}$,attained by the particle at subsequent times is . . . . . .

Two long parallel plates $A$ and $B$ are separated by a distance of $4 \ cm$ with an electric field of $45.5 \ Vm^{-1}$ between the plates directed normally from plate $A$ to plate $B$,as shown in the figure. An electron is projected from plate $A$ with velocity $v$ at an angle of $30^{\circ}$ with the surface of plate $A$. The maximum value of $v$ so that the electron does not hit plate $B$ is (Assume gravity-free space,charge of electron $= 1.6 \times 10^{-19} \ C$ and mass of electron $= 9.1 \times 10^{-31} \ kg$): (in $km \ s^{-1}$)

$A$ small point mass carrying some positive charge is released from the edge of a table. There is a uniform electric field in this region in the horizontal direction. Which of the following options correctly describes the trajectory of the mass? (Curves are drawn schematically and are not to scale).

$A$ charged spherical drop of mercury is in equilibrium in a plane horizontal air capacitor and the intensity of the electric field is $6 \times 10^4 \ Vm^{-1}$. The charge on the drop is $8 \times 10^{-18} \ C$. The radius of the drop is $\left[ \rho_{air} = 1.29 \ kg/m^3, \rho_{Hg} = 13.6 \times 10^3 \ kg/m^3, g = 9.8 \ m/s^2 \right]$.

An electron experiences a force equal to its weight when placed in an electric field. The intensity of the field will be