$A$ 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 $\text{ ms}^{-1}$)

In a parallel plate air capacitor,a cathode beam comprising $n = 10^6$ electrons is emitted with a velocity $v_0 = 10^8\ m/s$ into the space between the plates. The potential difference between the plates is $\phi = 400\ V$,the separation between the plates is $d = 2\ cm$ and the area of each plate is $l^2 = 100\ cm^2$ (where $l$ is the length of the plate). The deflection of the electron beam is ........... $mm$.

In a region of uniform electric field of intensity $E$,an electron of mass $m_e$ is released from rest. The distance travelled by the electron in a time $t$ is

An oil drop having charge $2e$ is kept stationary between two parallel horizontal plates $2.0 \, cm$ apart when a potential difference of $12000 \, V$ is applied between them. If the density of oil is $900 \, kg/m^3$,the radius of the drop will be

$A$ particle having mass $m$ and charge $q$ is at rest. On applying a uniform electric field $E$ on it,it starts moving. When this particle travels a distance $x$ in the direction of the force,its kinetic energy will be . . . . . . .

In an ink-jet printer,an ink droplet of mass $m$ is given a negative charge $q$ by a computer-controlled charging unit,and then enters at speed $v$ in the region between two deflecting parallel plates of length $L$ separated by distance $d$ (see figure below). All over this region exists a downward electric field $E$ which you can assume to be uniform. Neglecting the gravitational force on the droplet,the maximum charge that can be given so that it will not hit a plate is close to :