This occurs, for example, in the electromagnet core

Something like this

http://www.powerguru.org/wordpress/wp-content/uploads/2012/08/Magnetic-concentrators-used-in-Minisens.jpg

This occurs, for example, in the electromagnet core

Something like this

http://www.powerguru.org/wordpress/wp-content/uploads/2012/08/Magnetic-concentrators-used-in-Minisens.jpg

This method is also used to make magnetic lens for electron focussing. The principle is the same but the geometry is a little different.

Thank you for your responses, but I need something a little bit different.

Let say I have a sphere, I need to have high flux density somewhere inside the sphere and low flux density at the surface, and I cannot put anything inside the sphere, the source (e.g. electric current) should be outside of the sphere.

It may be that the answer you look for lies in the modern installation topologies for spheric plasma confinement. The solution seems to be difficult since magnetic fields always close through the smallest path, there is a magnetic permeability detail since these fields are found to media with high u and also media (conductive ones mostly) tend to answer to variable field with an opposing one in order to decrease H.

Magnetic flux density is a property of any magnetic material and the strength or intensity of the magnetic field varies (or drops off) with distance from the source or surface of the material. Thus for any source of magnetic field placed externally at the surface of a sphere the magnetic field strength and hence flux density will be greater than at the centre. If one has a very small sphere this might not make much difference but as the diameter of the sphere increases then the flux density at the centre will fall off more significantly.

Thus as I understand matters what you are asking appears to be in conflict with the basic laws. Magnetic fields have to start and end on the source (curl) and thus cannot be more intense at a distance than at the surface. For this the source will have to be within the sphere but which is contrary to your needs, which might be unrealistic.

If understand you correctly you would like to place (say) two magnets on either side of a sphere and then have some means of focusing so that the field intensity ("flux density") between them within the sphere is higher at the centre than at the surface.

This might be possible if there was (say) a gas with a higher relative permeability than the magnets.

This is how transformers and motors work in that the weak magnetic field around the primary conductors (H) excites or induces magnetic fields within the iron core ~10000 times stronger than in air. This is due the flux density (B) in iron being ~10000 stronger that of air. So your needs are somewhat the reverse of this.

Mircea above has shown that the concentrator involves using a material. As the flux density of the material is constant then the field intensity is controlled by varying the surface area as Flux =Flux Density / Area

Otherwise I might be missing something.