magnetic field

Hello ravikumar,

There are two answers to your question:

The simple answer is that they differ only in a constant, the magnetic permeability. For most of the applications you do not need anything more.

The complicated answer comes if you study differtial geometry, and you work with manifods (which are roughly curved spaces which locally look like Euclidean space - like the surface of a sphere). On manifolds B and H have a totally different geometrical character, namely H is a one-form (something which you integrate over a curve), and B is a two-form (something which you integrate over a surface). If you want to use the Maxwell equations in curved spacetime (wich was the very basic of the theory of realtivity by Einstein), you should be aware of these differences. In Gauss laws you integrate B and D (wich is also a two-form) over closed surfaces to get the amount of magnetic/electric charge inside the surface. In the Maxwell-Faraday equation you integrate E (which is a one-form) over a closed curve to get the change of B over the surface inside the curve. And in Ampere law you integrate H over a closed curve to get the change of D over the surface inside the curve. So roughly speaking B and D are connected with surfaces, E and H are connected with curves. In Euclidean space the difference between one-forms and two forms vanis, and all of them look like a vector (though neither of them is a vector truly). That is the basis of the awkward notation that you use two measures (B and H) for the same magnetic field. But if you do no research in relativity you will most likely not need to differentiate between them.

Andras