How is the field inside a rod magnet in the presence of ferro magnetic material?

[yungman]

For a rod magnet, how is the field inside the rod change if another piece of ferro magnetic material is being brought close to one end of the rod? Does the presence of ferro magnetic material increase the field strength inside the rod magnet?

 

[Hassan2]

For a rod magnet, how is the field inside the rod change if another piece of ferro magnetic material is being brought close to one end of the rod? Does the presence of ferro magnetic material increase the field strength inside the rod magnet?

Interesting question. Thanks.
Short answer: It increases the field inside.

A permanent magnet is nothing but a piece of saturated ferromagnetic material with a constant magnetization M. Inside the magnet, B=μ₀(H+M). When there is no source current, H=H_d , called demagnetizing field or stray field, which arises from magnetic dipoles. Has a decreasing effect on B ( roughly H_d=-NM , N being called demagnetizing factor. http://en.wikipedia.org/wiki/Demagnetizing_field
When a piece of ferromagnetic material is brought close to the magnet, the dipoles in the material are also partially aligned and will create their own field which affect the H_d inside the magnet too. Considering the polarity of the magnetization in the piece of magnetic material, The H_d inside the magnet decreases hence B increases. In the limit. the maximum possible B inside the magnet is when H_d=0.

 

[yungman]

Thanks for the reply, that is very helpful.

 

[Hassan2]

You're welcome.

I found an easier explanation based on equivalent surface and current densities rather than dipoles:
In a ferromagnetic material, including magnets , the equivallent volume current density is equal to $\nabla$$\times$M and the surface current density is equal to M$\times$n ( n is the outward normal to the surface). For a cylindrical magnet with its magnetization along z-axix , the volume current density is zero. the surface current have magnitude of M and the direction of a_$\phi$. This is like having a solenoid. When the ferromagnetic material is brought close to one of the magnet poles, the induced M inside it has equivalent currents too. Although M inside the body is not as uniform as in the magnet, it has a surface current in the same direction as the magnets current as well as some volume currents too. Altogether, the body acts like another solenoid and its field is superposed with the with magnets own field, increasing it.