Eight small drops,each of radius $r$ and having same charge $q$,are combined to form a big drop. The ratio between the potentials of the bigger drop and the smaller drop is

$A$ charge $+q$ is fixed at each of the points $x = x_0, x = 3x_0, x = 5x_0, \dots$ up to $\infty$ on the $X$-axis and a charge $-q$ is fixed at each of the points $x = 2x_0, x = 4x_0, x = 6x_0, \dots$ up to $\infty$. Here $x_0$ is a positive constant. Taking the potential at a point due to a charge $Q$ at a distance $r$ from it to be $\frac{Q}{4\pi\varepsilon_0 r}$,find the potential at the origin due to the above system of charges.

$A$ regular hexagon of side $10 \text{ cm}$ has a charge of $1 \mu\text{C}$ at each of its vertices. The potential at the centre of the hexagon is $\left[\frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \text{ SI unit}\right]$.

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 $P$.

Can the potential function have a maximum or minimum in free space? Explain.

An electron of charge $e$ coulomb passes through a potential difference of $V$ volts. Its energy in joules will be