$A$ charge of $10^{-3} \ \mu C$ is placed at the origin $(0, 0)$ of an $X-Y$ coordinate system. Two points $A$ and $B$ are located at $(\sqrt{2}, \sqrt{2})$ and $(2, 0)$ respectively. The potential difference between points $A$ and $B$ is ....... $V$.

If the electric potential of the inner metal sphere of radius $a$ is $10 \text{ V}$ and that of the outer spherical shell of radius $b$ is $5 \text{ V}$,then the potential at the centre will be ...... $\text{V}$.

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):

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 $m$)

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