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Here, the free currents or the current you can control is producing a magnetic field $\vec{B_0}$, outside the given system. So, the auxiliary field will be $ \vec{H} = B_0/\mu_0$ outside the material. Using the equations mentioned above you need to find magnetisation vector $ \vec{M} $ and total magnetic field $ \vec{B}$. As you have mentioned the auxiliary field inside the material due to the constant magnetisation vector only is $ - \vec{M}/3$. Therefore in this case the total auxiliary field inside the material is $ \vec{H} = (\vec{B_0}/\mu_0) - (\vec{M}/3)$.

Here, the free currents or the current you can control is producing a magnetic field $\vec{B_0}$, outside the given system. So, the auxiliary field will be $ \vec{H} = B_0/\mu_0$ outside the material. Using the equations mentioned above you need to find magnetisation vector $ \vec{M} $ and total magnetic field $ \vec{B}$ inside the material. As you have mentioned the total magnetic field and auxiliary field inside the material due to the constant magnetisation vector only are $ 2\mu_0 \vec{M}/3$ and $ - \vec{M}/3$, respectively. Therefore in this case the total auxiliary field inside the material is $ \vec{H} = (\vec{B_0}/\mu_0) - (\vec{M}/3)$.

2. The master equation in magnetostatics: $$ \vec{H} = \vec{B}/\mu_0 - \vec{M}. $$

2. The master equation in magnetostatics: $$ \vec{H} = (\vec{B}/\mu_0) - \vec{M}. $$

Here, auxiliary field $ \vec{H} $ is given as $B_0/\mu_0$ outside the material. Using the equations mentioned above you need to find magnetisation vector $ \vec{M} $ and total magnetic field $ \vec{B}$. As you have mentioned the magnetic field inside the material due to the constant magnetisation vector only is $ - \vec{M}/3$. Therefore in this case the total auxiliary field inside the material is $ \vec{H} = (\vec{B_0}/\mu_0) - (\vec{M}/3)$.

Here, the free currents or the current you can control is producing a magnetic field $\vec{B_0}$, outside the given system. So, the auxiliary field will be $ \vec{H} = B_0/\mu_0$ outside the material. Using the equations mentioned above you need to find magnetisation vector $ \vec{M} $ and total magnetic field $ \vec{B}$. As you have mentioned the auxiliary field inside the material due to the constant magnetisation vector only is $ - \vec{M}/3$. Therefore in this case the total auxiliary field inside the material is $ \vec{H} = (\vec{B_0}/\mu_0) - (\vec{M}/3)$.