On moving a charge of $20$ coulombs by $2 \;cm , 2 \;J$ of work is done, then the potential difference between the points is (in $volt$)

Electric field at a place is $\overrightarrow {E\,}  = {E_0}\hat i\,V/m$ . A particle of charge $+q_0$  moves from point $A$ to $B$ along a circular path find work done in this motion by electric field 

Consider a system of three charges $\frac{\mathrm{q}}{3}, \frac{\mathrm{q}}{3}$ and $-\frac{2 \mathrm{q}}{3}$ placed at points $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$, respectively, as shown in the figure,

Take $\mathrm{O}$ to be the centre of the circle of radius $\mathrm{R}$ and angle $\mathrm{CAB}=60^{\circ}$

Figure:$Image$ 

A particle of mass $100\, gm$ and charge $2\, \mu C$ is released from a distance of $50\, cm$  from a fixed charge of $5\, \mu C$. Find the speed of the particle when its distance  from the  fixed charge becomes $3\, m$. Neglect any other force........$m/s$

A particle of mass $m$ having negative charge $q$ move along an ellipse around a fixed positive charge $Q$ so that its maximum and minimum distances from fixed charge are equal to $r_1$ and $r_2$ respectively. The angular momentum $L$ of this particle is

A disk of radius $R$ with uniform positive charge density $\sigma$ is placed on the $x y$ plane with its center at the origin. The Coulomb potential along the $z$-axis is

$V(z)=\frac{\sigma}{2 \epsilon_0}\left(\sqrt{R^2+z^2}-z\right)$

A particle of positive charge $q$ is placed initially at rest at a point on the $z$ axis with $z=z_0$ and $z_0>0$. In addition to the Coulomb force, the particle experiences a vertical force $\vec{F}=-c \hat{k}$ with $c>0$. Let $\beta=\frac{2 c \epsilon_0}{q \sigma}$. Which of the following statement($s$) is(are) correct?

$(A)$ For $\beta=\frac{1}{4}$ and $z_0=\frac{25}{7} R$, the particle reaches the origin.

$(B)$ For $\beta=\frac{1}{4}$ and $z_0=\frac{3}{7} R$, the particle reaches the origin.

$(C)$ For $\beta=\frac{1}{4}$ and $z_0=\frac{R}{\sqrt{3}}$, the particle returns back to $z=z_0$.

$(D)$ For $\beta>1$ and $z_0>0$, the particle always reaches the origin.