Three charges each of value $+q$ are placed at the corners of an isosceles triangle $ABC$ with sides $AB = AC = 2a$. The midpoints of $AB$ and $AC$ are $D$ and $E$ respectively. The work done in taking a charge $Q$ from $D$ to $E$ is (where $\varepsilon_0$ is the permittivity of free space):

Figures $(a)$ and $(b)$ show the field lines of a positive and negative point charge respectively.
$(a)$ Give the signs of the potential difference $V_{P}-V_{Q}$ and $V_{B}-V_{A}$.
$(b)$ Give the sign of the potential energy difference of a small negative charge between the points $Q$ and $P$,and $A$ and $B$.
$(c)$ Give the sign of the work done by the field in moving a small positive charge from $Q$ to $P$.
$(d)$ Give the sign of the work done by the external agency in moving a small negative charge from $B$ to $A$.
$(e)$ Does the kinetic energy of a small negative charge increase or decrease in going from $B$ to $A$?

$A$ point charge $q$ is surrounded by eight identical charges,each of magnitude $q$,at a distance $r$ as shown in the figure. How much work is done by the forces of electrostatic repulsion when the point charge at the center is moved to infinity?

An electric charge $10^{-6} \mu C$ is placed at the origin $(0,0) \text{ m}$ of an $X-Y$ coordinate system. Two points $P$ and $Q$ are situated at $(\sqrt{3}, \sqrt{3}) \text{ m}$ and $(\sqrt{6}, 0) \text{ m}$ respectively. The potential difference between the points $P$ and $Q$ will be:

Two electric charges of $9 \mu C$ and $-3 \mu C$ are placed $0.16 \ m$ apart in air. There will be a point $P$ on the line joining the two charges and between them where the electric potential is zero. The distance of $P$ from the $9 \mu C$ charge is: (in $m$)

Define electrostatic potential energy.