jdalrymple/html-to-latex

\documentclass{article}
 
\usepackage{amsmath}
\usepackage{graphicx}
 
 
\begin{document}
 
Three concentric metal shells \(A,{\rm{ }}B\) and \(C\) of respective radii \(a,{\rm{ }}b\) and \(c\) \((a < b < c)\) have surface charge densities \( + \sigma , - \sigma \) and \( + \sigma \) respectively. The potential of shell \({\rm{B}}\) is:
 
\begin{center}
    \includegraphics{images/image2.png}
\end{center}
 
Net potential at \({\rm{B}}\) is due to superposition of plotential due to all shells.
 
\({V_B} = {V_{B(I)}} + {V_{B(II)}} + {V_{B(III)}}\)
 
\( = \cfrac{{K4\pi {a^2}\sigma }}{b} + \cfrac{{K4\pi {b^2}( - \sigma )}}{b} + \cfrac{{K4\pi {c^2}(\sigma )}}{c}\)
 
Required potential of b
 
\( = \cfrac{{\sigma {a^2}}}{{{\varepsilon _0}b}} - \cfrac{{\sigma {b^2}}}{{{\varepsilon _0}b}} + \cfrac{{\sigma {c^2}}}{{{\varepsilon _0}c}}\)
 
\( = \cfrac{\sigma }{{{\varepsilon _0}}}\left( {\cfrac{{{a^2} - {b^2}}}{b} + c} \right)\)
 
 
\end{document}