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 identical thin rings each of radius $R \text{ m}$ are kept on the same axis at a distance of $R \text{ m}$ apart. If the charges on them are $10 \text{ C}$ and $5 \text{ C}$ respectively,calculate the work done in moving a charge '$q$' coulomb from the centre of one ring to that of another.

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.)

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 $x=a+r$ (if $a << r$) is: ($\varepsilon_0$ is the permittivity of free space)

The potential difference between the center and the surface of a sphere of radius $R$ with a uniform volume charge density $\rho$ within it will be:

$A$ spherical drop of liquid carrying charge $Q$ has potential $V_0$ at its surface. If two drops of same charge and radius combine to form a single spherical drop,then the potential at the surface of the new drop is (Assume $V=0$ at infinity.)