Write the equation of the magnetic field obtained in the core of a solenoid in the form of $\vec{H}$ and $\vec{M}$.

(N/A) The total magnetic field $\vec{B}$ inside the core of a solenoid is the sum of the magnetic field due to the current in the solenoid windings $(\vec{B}_0)$ and the magnetic field due to the magnetization of the material $(\vec{B}_m)$.
Mathematically,this is expressed as:
$\vec{B} = \vec{B}_0 + \vec{B}_m$
Since $\vec{B}_0 = \mu_0 \vec{H}$ and $\vec{B}_m = \mu_0 \vec{M}$,where $\vec{H}$ is the magnetic intensity and $\vec{M}$ is the magnetization of the material,we can write:
$\vec{B} = \mu_0 \vec{H} + \mu_0 \vec{M}$
$\vec{B} = \mu_0 (\vec{H} + \vec{M})$