I'm confused between them. Can someone explain the difference between them? Is $\vec H$ field only relevant during magnetization or demagnetization? $\vec H$ is just that value needed to magnetize/demagnetize or what is it useful for?
Is $\vec H$ only relevant to solenoids or magnets as well? Does it make sense to state a magnet has a field of $0.5~\mathrm T$ and a field strength $\vec H$ of $9\times10^5~\mathrm{ A/m}$?
Yeah! $\vec{B}$ and $\vec{H}$ seems to be same and confusing, but they are two different quantities (Look at their units).
Electric current $I$ produces around itself magnetic field strength "$\vec{H}$" (also called as "Magnetic field intensity") regardless the type of the surrounding medium. "Magnetic Flux density" "$\vec{B}$" is a response of the medium to the applied excitation $\vec{H}$.
Also you must have come across the equation, which must have caused the doubt i.e $\vec{B}=\mu_0\vec{H}$ The true equation is "$\vec{B}=\mu_0(\vec{H}+\vec{M})$"
$\vec{M}$= Magnetization,
for free space, Magnetization is $0$ so $\vec{B}=\mu_0 \vec{H}$
Look at the definition of $\vec{H}$. It is equal to $\vec{B}/\mu_0-\vec{M}$ with $\vec{M}$ the magnetization. Its main use comes from the fact that $\vec{\nabla}\times\vec{H}=\vec{J}_\textrm{free}$ (in the static case). Seeing as we are usually only able to accurately control free currents (as opposed to induced ones in the material), this formula is quite useful.
Note that, outside of a material (in the vacuum), $\vec{H}=\vec{B}/\mu_0$, so if you like you could use $\vec{H}$ in all of the equations where you'd normally use $\vec{B}$, getting rid of the usual factor $\mu_0$ that appears virtually always when dealing with magnetism. For a much more elaborate explanation, look at chapter 6 of Griffith's standard undergrad textbook.
