$A$ charged oil drop is suspended in a uniform electric field of $3 \times 10^{4} \; V/m$ so that it neither falls nor rises. The charge on the drop will be $..... \times 10^{-18} \; C$. (Take the mass of the drop $= 9.9 \times 10^{-15} \; kg$ and $g = 10 \; m/s^{2}$)

$A$ particle with charge $q$ approaches a fixed particle with charge $Q$ with an initial velocity $v$. It comes to a stop at a closest distance $r$ from $Q$. If the particle $q$ is given an initial velocity $2v$,the closest distance will be:

An electron is accelerated through a potential difference $(p.d.)$ of $45.5 \ V$. The velocity acquired by it is (in $m \ s^{-1}$)

An electron enters a parallel plate capacitor with horizontal speed $u$ and is found to deflect by angle $\theta$ on leaving the capacitor as shown below. It is found that $\tan \theta = 0.4$ and gravity is negligible. If the initial horizontal speed is doubled, then the value of $\tan \theta$ will be

An electron and a positron enter a uniform electric field $E$ perpendicular to it with equal speeds at the same time. The distance of separation between them in the direction of the field after a time $t$ is (where $\frac{e}{m}$ is the specific charge of the electron).

An electron with kinetic energy $K_{1}$ enters between parallel plates of a capacitor at an angle $\alpha$ with the plates. It leaves the plates at an angle $\beta$ with the plates. If the kinetic energy of the electron when leaving is $K_{2}$,then the ratio of kinetic energies $K_{1}:K_{2}$ is ....... .