Magnetic Scalar and Vector Potentials:
In studying electric field problems, we introduced the concept of electric potential that simplified the computation of electric fields for certain types of problems. In the same manner let us relate the magnetic field intensity to a scalar magnetic potential and write:
...................................(4.21)
From Ampere's law , we know that
......................................(4.22)
Therefore, 
............................(4.23)
But using vector identity, 
we find that 
is valid only where 
. Thus the scalar magnetic potential is defined only in the region where . Moreover, Vm in general is not a single valued function of position.