There is $10$ units of charge at the centre of a circle of radius $10\,m$. The work done in moving $1\, unit$ of charge around the circle once is………..$units$

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.

Hydrogen ion and singly ionized helium atom are accelerated, from rest, through the same potential difference. The ratio of final speeds of hydrogen and helium ions is close to……

The work which is required to be done to make an arrangement of four particles each having a charge $+q$ such that the particles lie at the four corners of a square of side $a$ is …….

The charge given to any conductor resides on its outer surface, because