What Is the Difference Between H Field and B Field in a Solenoid?

[anon6912]

This is a slide from my lecture illustrating how to find the magnetic field in a solonoid with an air gap.

I don't quite understand the following points:
What is the H field?
Whats the difference between the H field and the B field?
Why do you need them?

Other than that i understand how to do the integral and the evaluation. I just don't understand what the H field is.

EDIT: I attached a nother slide about the H field

 

[indie452]

H is the magnetic field strength while B is the flux density. The strict definition of H is

H = B / μ0 - M where M is the magnetisation

However it is usually possible to simplify the calculation

H = B / μ

look at http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magfield.html or search for "magnetic field strength H" and you will most likely find what you need