Two charges $q_1$ and $q_2$ are fixed at points $A$ and $B$ respectively, separated by a distance of $30 \text{ cm}$. $A$ third charge $q_3$ is moved along a circular path of radius $40 \text{ cm}$ from point $C$ to point $D$. If the difference in potential energy due to the movement of $q_3$ from $C$ to $D$ is $q_3 K / (4 \pi \epsilon_0)$, find the value of $K$. (Given: $AC = 40 \text{ cm}$, $AB = 30 \text{ cm}$, $AD = 40 \text{ cm}$)

Two point charges $-q$ and $+q$ are located at points $(0,0,-a)$ and $(0,0, a)$ respectively. The electric potential at a point $(0,0, z)$,where $z>a$ is

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 $q$ of mass $m$ is placed at the center of a ring of radius $R$ carrying a charge $Q$. When it is slightly displaced,the point charge accelerates to infinity along the $x$-axis. The ultimate speed of the point charge is .......

Two charges $3 \times 10^{-8} \; C$ and $-2 \times 10^{-8} \; C$ are located $15 \; cm$ apart. At what point on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.

Which of the following graphs correctly shows how the electrostatic potential $V$ varies with distance $r$ from a point charge?