$A$ positively charged ring is in the $y-z$ plane with its centre at the origin. $A$ positive test charge $q_0$,held at the origin,is released along the $x$-axis. Then its speed

$A$ regular hexagon of side $10 \text{ cm}$ has a charge of $1 \mu\text{C}$ at each of its vertices. The potential at the centre of the hexagon is $\left[\frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \text{ SI unit}\right]$.

Four charges are arranged at the corners of a square $ABCD$ of side $d$,as shown in Figure.
$(a)$ Find the work required to put together this arrangement.
$(b)$ $A$ charge $q_{0}$ is brought to the centre $E$ of the square,the four charges being held fixed at its corners. How much extra work is needed to do this?

A charge $+q$ is fixed at each of the points $x = x_0, x = 3x_0, x = 5x_0, \dots, \infty$ on the $x$-axis, and a charge $-q$ is fixed at each of the points $x = 2x_0, x = 4x_0, x = 6x_0, \dots, \infty$. Here $x_0$ is a positive constant. Take the electric potential at a point due to a charge $Q$ at a distance $r$ from it to be $Q/(4\pi\varepsilon_0 r)$. Then, the potential at the origin due to the above system of charges is:

An electric charge $10^{-3} \mu C$ is placed at the origin of $x-y$ plane. The potential difference between points $A$ and $B$ located at $(\sqrt{2} m, \sqrt{2} m)$ and $(2 m, 0 m)$ respectively is (in $V$)

The work done in carrying a charge $Q$ once around a circle of radius $r$ about a charge $q$ at the centre is