Twenty-seven drops of water of the same size are equally and similarly charged. They are then united to form a bigger drop. By what factor will the electrical potential change?

Two point charges $4q$ and $-q$ are fixed on the $x$-axis at $x = -d/2$ and $x = d/2$,respectively. If a third point charge $q$ is moved from the origin to $x = d$ along the semicircle as shown in the figure,the potential energy of the charge will:

$A$ hollow metal sphere is charged with a charge of $3.2 \times 10^{-19} \ C$. If the radius of the sphere is $10 \ cm$,then the electric potential at a distance of $4 \ cm$ from its center will be:

$A$ charge of $8 \; mC$ is located at the origin. Calculate the work done in $J$ in taking a small charge of $-2 \times 10^{-9} \; C$ from a point $P (0, 0, 3 \; cm)$ to a point $Q (0, 4 \; cm, 0)$,via a point $R (0, 6 \; cm, 9 \; cm)$.

$A$ small sphere of radius $r_{1}$ and charge $q_{1}$ is enclosed by a spherical shell of radius $r_{2}$ and charge $q_{2}$. Show that if $q_{1}$ is positive,charge will necessarily flow from the sphere to the shell (when the two are connected by a wire) no matter what the charge $q_{2}$ on the shell is.

There are four concentric shells $A, B, C$ and $D$ of radii $a, 2a, 3a$ and $4a$ respectively. Shells $B$ and $D$ are given charges $+q$ and $-q$ respectively. Shell $C$ is now earthed. The potential difference $V_A - V_C$ is: