Module 1 : Electromagnetic waves
Lecture 2: Solving static boundary value problems
2. Separation of variables for
(contd..)
Spherical polar coordinates
(7)
Form of the solution
if the solution is to be finite at infinity,
if it is to be finite at the origin
associated Legendre polynomials
magnitudes of spherical harmonics
if the solution is finite along z axis, since
blows up there
Azimuthal symmetry
m = 0
single-valued solution
E = 0
, Legendre polynomials
(contd..)
if the solution is to be finite at infinity,
if it is to be finite at the origin
associated Legendre polynomials
magnitudes of spherical harmonics
if the solution is finite along z axis, since 
blows
up there
m = 0
single-valued solution 
, Legendre polynomials