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 $V$)

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: $AC = 40 \text{ cm}$, $AB = 30 \text{ cm}$, $AD = 40 \text{ cm}$)

Along the $x$-axis,three charges $\frac{q}{2}, -q$ and $\frac{q}{2}$ are placed at $x=0, x=a$ and $x=2a$ respectively. The resultant electric potential at a point $P$ located at a distance $r$ from the charge $-q$ $(r > a)$ is ($\varepsilon_0$ is the permittivity of free space):

The radius of a soap bubble whose potential is $16\,V$ is doubled. The new potential of the bubble will be.....$V$

Eight charges,each of magnitude $q$,are placed at the vertices of a cube placed in a vacuum. The electric potential at the centre of the cube due to this system of charges is . . . . . . . ($\varepsilon_0 = $ permittivity of vacuum,$a = $ length of each side of the cube.)

The side length of an equilateral triangle is $d$. Three charges,each of magnitude $Q$,are placed at the three vertices. If $P$ is the midpoint of one side,find the electric potential $V_P$ at point $P$.