# Magnetic vector and scalar potential

I understood that
curl H = J
H being magnetic field intensity and magnetic flux density B = u H (u being permeability of free space)
divergence of B is zero because isolated magnetic charge or pole doesn't exist.
but then they define magnetic scalar and vector potentials .i can imagine H and B like in terms of field lines but this scalar and vector potentials making me very uncomfortable.
They say H= - del Vm
(negative divergence of scalar potential) and this is valid only when current density J=0. What i undertood is, first of all static magnetic field is produced by constant current if current density is zero which is del I / del S then current is zero then how can magnetic field exist at first place.
And then they define magnetic vector potential (A) exist just because del . B =0(div of B =0) so B can be expressed as curl of some function since divergence of curl of a vector is zero . I understand this in terms of vector identities but m not able to imagine this magnetic vector potential.
Some body please explain this. Any link to a simulation or java applet will be very helpfull . . .
Thank u.

My understanding is those scalar magnetic potential are fake terms that is used only to make it more convenient in certain calculation. They are trying to make it similar the scalar electric potential of $\vec E=-\nabla V$. It is not really existing. You only have vector magnetic potential A and $\vec B =\nabla \times \vec A$.

I never really study the scalar magnetic potential as it is not real.

ok. So how can vector magnitude potential be defined like in layman terms other than telling that curl of magnetic vector potential gives magnetic flux density.

I study EM but I am not an expert, but I don't think they ever explain in layman's term. It is more like because $\nabla \cdot \vec B \equiv 0\;\; \Rightarrow \;\vec B \;\hbox { is solenoidal} \;\Rightarrow \vec B = \nabla \times \;\hbox { (a vector field).}$ This is the Helmholtz's Theorem. Google this and you'll have a better understanding of the irrotational and solenoidal. And they defined the vector field as "vector magnetic potential" A.

As I said, I am not an instructor nor expert, double check what I said. It should be easy to verify. Just look at your text book and you should find it. This is basic static magnetics.

Last edited:
thanks alot. . .Ill do that
:-)