Here's my understanding (although I am not too qualified): the magnetic flux density $\text{d}\bf{B}$ due to a current element $I\text{d}\bf{s}$ at a position $\bf{r}$ relative to this current element is given by the Biot-Savart Law

$\text{d}\textbf{B} = \frac{\mu_0 I}{4\pi r^3} (\text{d}\textbf{s} \times \textbf{r})$

which is indeed independent of any material which lies between the current element and the point of interest $\textbf{r}$. It only depends on the current elements present and their distance from your point of interest.

As for your second question: the H field is defined by

$\textbf{H} = \frac{\textbf{B}}{{\mu_0}} - \textbf{M}$

Where $\textbf{M}$ is the magnetisation per unit volume of the material. It is material dependent and I'm sure there's lots of unusual materials that have weird magnetisations. However for the most part we assume that all 3 of these fields are parallel, and that $\textbf{M}$ is linearly proportional to $\text{H}$. That allows you to write $\textbf{B} = \mu \textbf{H}$ for some constant $\mu$ which we call the permeability of the medium.

So to answer your question: if one had full knowledge of how the material you are within behaved, i.e. you fully understood its magnetisation, then the H field would be 'distinct' from the B field (in the sense that they are not just constants away from each other).

P.S. I'm not too sure how mu-metals work. There is an example in Bleaney & Bleaney of a sphere within a H field & I assume you could generalise this to a sphere within a shell within a field, and then set the permeability of the shell to be very high, in order to get the H field (and then also the B field - although this derivation does make some assumptions about the magnetisation which may not be valid.)

P.P.S. Reading Bleaney & Bleaney is always a good idea if you wish to understand EM more.

Source for Biot-Savart formula: Electricity & Magnetism by Bleaney & Bleaney 3rd edition Section 4.1 e.g. page 100 here

Here's my understanding (although I am not too qualified): the magnetic flux density $\text{d}\bf{B}$ due to a current element $I\text{d}\bf{s}$ at a position $\bf{r}$ relative to this current element is given by the Biot-Savart Law

$\text{d}\textbf{B} = \frac{\mu_0 I}{4\pi r^3} (\text{d}\textbf{s} \times \textbf{r})$

which is indeed independent of any material which lies between the current element and the point of interest $\textbf{r}$. It only depends on the current elements present and their distance from your point of interest. (However, if there is a magnetisable material nearby, this B field will produce induced magnetic dipoles within that material, which will then in turn affect the overall B field.)

As for your second question: the H field is defined by

$\textbf{H} = \frac{\textbf{B}}{{\mu_0}} - \textbf{M}$

Where $\textbf{M}$ is the magnetisation per unit volume of the material. It is material dependent and I'm sure there's lots of unusual materials that have weird magnetisations. However for the most part we assume that all 3 of these fields are parallel, and that $\textbf{M}$ is linearly proportional to $\text{H}$. That allows you to write $\textbf{B} = \mu \textbf{H}$ for some constant $\mu$ which we call the permeability of the medium.

So to answer your question: if one had full knowledge of how the material you are within behaved, i.e. you fully understood its magnetisation, then the H field would be 'distinct' from the B field (in the sense that they are not just constants away from each other).

P.S. I'm not too sure how mu-metals work. There is an example in Bleaney & Bleaney of a sphere within a H field & I assume you could generalise this to a sphere within a shell within a field, and then set the permeability of the shell to be very high, in order to get the H field (and then also the B field - although this derivation does make some assumptions about the magnetisation which may not be valid.)

P.P.S. Reading Bleaney & Bleaney is always a good idea if you wish to understand EM more.

Source for Biot-Savart formula: Electricity & Magnetism by Bleaney & Bleaney 3rd edition Section 4.1 e.g. page 100 here

Here's my understanding (although I am not too qualified): the magnetic flux density $\text{d}\bf{B}$ due to a current element $I\text{d}\bf{s}$ at a position $\bf{r}$ relative to this current element is given by the Biot-Savart Law

$\text{d}\textbf{B} = \frac{\mu_0 I}{4\pi r^3} (\text{d}\textbf{s} \times \textbf{r})$

which is indeed independent of any material which lies between the current element and the point of interest $\textbf{r}$. It only depends on the current elements present and their distance from your point of interest.

As for your second question: the H field is defined by

$\textbf{H} = \frac{\textbf{B}}{{\mu_0}} - \textbf{M}$

Where $\textbf{M}$ is the magnetisation per unit volume of the material. It is material dependent and I'm sure there's lots of unusual materials that have weird magnetisations. However for the most part we assume that all 3 of these fields are parallel, and that $\textbf{M}$ is linearly proportional to $\text{H}$. That allows you to write $\textbf{B} = \mu \textbf{H}$ for some constant $\mu$ which we call the permeability of the medium.

So to answer your question: if one had full knowledge of how the material you are within behaved, i.e. you fully understood its magnetisation, then the H field would be 'distinct' from the B field (in the sense that they are not just constants away from each other).

P.S. Reading Bleaney & Bleaney is always a good idea if you wish to understand EM more.

Source for Biot-Savart formula: Electricity & Magnetism by Bleaney & Bleaney 3rd edition Section 4.1 e.g. page 100 here

Here's my understanding (although I am not too qualified): the magnetic flux density $\text{d}\bf{B}$ due to a current element $I\text{d}\bf{s}$ at a position $\bf{r}$ relative to this current element is given by the Biot-Savart Law

$\text{d}\textbf{B} = \frac{\mu_0 I}{4\pi r^3} (\text{d}\textbf{s} \times \textbf{r})$

which is indeed independent of any material which lies between the current element and the point of interest $\textbf{r}$. It only depends on the current elements present and their distance from your point of interest.

As for your second question: the H field is defined by

$\textbf{H} = \frac{\textbf{B}}{{\mu_0}} - \textbf{M}$

Where $\textbf{M}$ is the magnetisation per unit volume of the material. It is material dependent and I'm sure there's lots of unusual materials that have weird magnetisations. However for the most part we assume that all 3 of these fields are parallel, and that $\textbf{M}$ is linearly proportional to $\text{H}$. That allows you to write $\textbf{B} = \mu \textbf{H}$ for some constant $\mu$ which we call the permeability of the medium.

So to answer your question: if one had full knowledge of how the material you are within behaved, i.e. you fully understood its magnetisation, then the H field would be 'distinct' from the B field (in the sense that they are not just constants away from each other).

P.S. I'm not too sure how mu-metals work. There is an example in Bleaney & Bleaney of a sphere within a H field & I assume you could generalise this to a sphere within a shell within a field, and then set the permeability of the shell to be very high, in order to get the H field (and then also the B field - although this derivation does make some assumptions about the magnetisation which may not be valid.)

P.P.S. Reading Bleaney & Bleaney is always a good idea if you wish to understand EM more.

Source for Biot-Savart formula: Electricity & Magnetism by Bleaney & Bleaney 3rd edition Section 4.1 e.g. page 100 here