Derive an expression for electric potential at a point due to a point charge.

A hollow metallic sphere of radius $0.2 \mathrm{m}$ is given a charge of $+15 \mathrm{\mu C}$. Find
(i) electric potential at its surface.
(ii) potential at its centre.
(iii) electric potential at $0.3 \mathrm{m}$ from centre.

Consider a particle with charge $q=3.0 \mathrm{nC}$, point $A$ at distance $d_1=2.0 \mathrm{m}$ from $q$ and the point $B$ at distance $d_2=1.0 \mathrm{m}$. If $A$ and $B$ are diametrically opposite to each other as in the figure, (a) what is the electric potential difference $V_{\mathrm{A}}-V_{\mathrm{B}}$? (b) what is the electric potential difference if $A$ and $B$ are located as in the figure (b)?

A spherical conductor of radius $12 \mathrm{cm}$ has a charge of $1.6\times {10}^{-7} \mathrm{C}$ distributed uniformly on its surface. What is the electric field at a point $18 \mathrm{cm}$ from the center of the sphere? Take, $\frac{1}{4\pi {\epsilon }_0}=9\times {10}^9 \mathrm{N} {\mathrm{m}}^2 {\mathrm{C}}^{-2}$