Eight equal charges $q$ are placed at each corner of a cube of side $a$. The work done in carrying a charge $-q$ from its centre to infinity is:

The figure shows a positively charged infinite wire. $A$ particle of charge $q = 2 \, C$ moves from point $A$ to $B$ with constant speed. (Given linear charge density on the wire is $\lambda = 4 \pi \varepsilon_0$)

Two point charges of $1 \text{ nC}$ and $2 \text{ nC}$ are placed at two corners of an equilateral triangle of side $3 \text{ cm}$. The work done in bringing a charge of $3 \text{ nC}$ from infinity to the third corner of the triangle is . . . . . . $\mu\text{J}$. $( \frac{1}{4\pi\epsilon_{0}} = 9 \times 10^{9} \text{ N.m}^{2}/\text{C}^{2} )$

At the centre of a half ring of radius $R=10 \ cm$ and linear charge density $\lambda = 4 \ nC \ m^{-1}$,the potential is $x \pi \ V$. The value of $x$ is . . . . .

An electrostatic paint sprayer has a metal sphere of diameter $18 \, cm$ and at a potential of $25 \, kV$. The charge on the metal sphere is: (in $ \, \mu C$)

$A$ regular hexagon of side $6 \ cm$ has a charge of $2 \ \mu C$ at each of its vertices. What is the potential at the centre of the hexagon? $\left[\frac{1}{4 \pi \epsilon_0}=9 \times 10^9 \text{ SI units}\right]$