Are both $B$ and $H$ used for magnetic field intensity?

Question

My teachers use $B$ for representing magnetic field and the standard textbooks do so as well, but recently, one of my friends said that $B$ is magnetic flux density, and $H$ is used to represent magnetic field.
I tried to look it up on the net and found both $H$ and $B$ are used for magnetic field. Can someone explain why are both used?
PS - I am currently only in grade 10 and have not been introduced to vectors or calculus(I know some of the basics though), and that is why I couldn't look up too much in detail.

rob · Accepted Answer

They're the same until you need them to be the same, at which point you discover they are slightly different. H is "the magnetic field," while B is "the magnetic induction."  However it's quite common to see B referred to as "the magnetic field" as well, because they are so similar.
H is what experimenters control with electromagnets; it is produced by moving free charges, according to the Biot-Savart rule.
B is what steers moving charged particles, according to the Lorentz force law. B includes contributions from free currents (that is, H) but also contributions from induced magnetic materials and permanent magnets. As GiorgioP elaborates in another answer, magnetic materials can be quite complicated and can do things like remember their pasts, so B and H may have a nonlinear relationship and may point in different directions.
If you have lived an especially sinful life, then you'll have to use the convention where B and H have different units, and you'll have to multiply by $mu$ or $mu_0$ to change from one to the other, even when there aren't materials effects.

GiorgioP · Answer

Rob's answer is correct, but it contains only half of the story.
If the only difference between $B$ and $H$ field would be a factor $mu$ or $mu_0$, or the role played in the Lorentz force or Ampère's law expression, it would be almost useless to introduce two distinct vector fields.
What makes unavoidable to have two fields is the need of formulating macroscopic electromagnetism in the presence of materials.
It turns out that in order to describe magnetic behavior in the presence of materials, one needs two different vector fields, $B$ and $H$ (but sometimes it could be preferable to express $H$ in term of a third vector field: the magnetization density $M$), which in general have neither a linear relation nor the same direction. The relation between $B$ and $H$ inside a material is in general a non-linear relation, depending on the material and its thermodynamic state.

Are both $B$ and $H$ used for magnetic field intensity?

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