A particle of mass $m$ and charge $-q$ is given velocity $v$ as shown in the figure. What minimum distance it can travel before stopping for the first time? $A$ and $B$ fixed charges. Given that $v=\sqrt{\frac{2KqQ}{am}}$ where $K=\frac{1}{4\pi {\epsilon }_0}$

Four charges are placed at the corners of a square of side $a.$

Work done by external agent in carrying an electron from point $O$ to $O^{\text{'}}$ is

In the figure, two points $\left(A\right)$ and $\left(B\right)$ are located within a region that contains an electric field. A negative charge is placed at $\left(A\right)$ and then moved to $\left(B\right).$ Does the potential energy of the system increase, decrease or remain same?

Two fixed solid spheres of charges $Q$ and $kQ$ are separated by a distance $6R.$ A charge $-q$ is to be projected along the line joining their centres, so that it can reach the surface of other solid sphere of charge $kQ.$

(i) If $k=4,$ find minimum velocity to be given.
(ii) If we do not want to give any velocity, what should be the minimum value of $k?$