Laplace’s equation(Magneto statics):-
From the equation .
we know that for zero current density , the Magnetic scalar potential is
by replacing in the equation ,
. is known as Laplce’s equation in Magneto statics.
Poisson’s equation(Magneto statics):-
In vector algebra a vector can be fully defined if it’s curl and divergence are defined.
-point form of Ampere’s law
from vector Magnetic potential .
from the vector identity .
– this equation is known as Poisson’s equation for Magneto statics.
by equating the respective components on each side
, and are the scalar Poisson’s equations of Magneto statics.