The electric field intensity near a conducting surface having uniform surface charge density ' $\sigma$ ' is given by ( $\varepsilon_0=$ permittivity of free space)

A regular hexagon of side 6 cm has a charge of $2 \mu \mathrm{C}$ at each of its vertices, what is the potential at the centre of the hexagon?

$$ \left[\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \text { SI unit }\right] $$

Three equal charges are placed on the three corners of a square as shown below. If the magnitude of force between ' $\mathrm{q}_1$ ' and ' $\mathrm{q}_2$ ' is ' $\mathrm{F}_{12}$ ' and that between ' $\mathrm{q}_1$ ' and ' $\mathrm{q}_3$ ' is $\mathrm{F}_{13}$, then the ratio of $F_{13}$ to $F_{12}$ is

Three charges each of magnitude $3 \mu \mathrm{C}$, are placed on the vertices of an equilateral triangle of side 6 cm . The net potential energy of the system will be nearly $\left[\frac{1}{4 \pi \epsilon_0}=9 \times 10^9\right.$ SI unit $]$