Part 1 : Nanoparticles Module 6 : Mie theory for Scattering and absorption by                    a sphere and ellipsoids
Lecture 2 : The solution for the fields
 
$B_{o1l}$ and $A_{e1l}$ can be evaluated explicitly (left as problem), and one gets
\begin{displaymath}B_{o1l}=E_l\,,\quad\quad A_{e1l} =-iE_l\,,\quad\quad E_l= E_o\,\frac{(2l+1)}{l(l+1)}i^l\,,\end{displaymath}
so that
\begin{displaymath}{\vec{E}}_i =\sum_{l=1}^\infty \,E_l\,\left[\vec M_{o1l}^{(1)}-i\vec N_{e1l}^{(1)}\right]\,.\end{displaymath}
The corresponding magnetic field is
\begin{displaymath}{\vec{H}}_i=\frac{1}{i\omega\mu}\,\vec{\nabla}\times{\vec{E}}... ...y \,E_l\,\left[\vec N_{o1l}^{(1)}-i\vec M_{e1l}^{(1)}\right]\,.\end{displaymath}
\begin{displaymath}{\rm Or}\quad\quad {\vec{H}}_i=-\frac{q}{\omega\mu}\,\sum_{l=... ...y \,E_l\,\left[\vec M_{e1l}^{(1)}+i\vec N_{o1l}^{(1)}\right]\,.\end{displaymath}