Why does the tangential component of the magnetic field increases inside a material?

Question

Let us suppose that there is a constant uniform magnetic field perpendicular to the surface of a block of iron. Why does the magnetic field increases inside the block? Is it due to the alignment of the small magnetic dipoles in the direction of magnetic field? If this is so, is it analogous to the field developed inside when a electric field is applied to a dielectric material? In the case of electric field, the field inside reduces by $\varepsilon_r$ times (where $\varepsilon_r$ denotes the relative permittivity of the dielectric material), Is it equally true in the case of magnetic field? Will the magnetic field increase by $\mu_r$ times? (where $\mu_r$ denotes the relative permeability of the material)

Answer 1

It sounds to me that you are describing a solid-core transformer. As Matteo correctly explained above the core material is all important in determining the express interactions between the magnetic field and the core.

You mentioned iron, which is a ferromagnetic material. And you mention tiny dipoles, which I assume you intended refer to them as being inside the iron. Remember iron is a base element.

And though there are various theories bantered about, magnetic flux does not necessarily work on a bipolar junction. It is simpler for the human mind to understand magnetic flux as a singular one-way street. Man made magnets themselves display what we refer to as bipolar movement. But that could be just a limitation of our human senses. That man-made magnet, by the way and for the most part is made using the idea that bipolar atoms are realigned in the magnet. And resultingly we see what appears to be two poles. Which is disheartening because it is misleading. Opposite poles appear to be repelling one another. When in fact they are merely interrupting the magnetic flux stream of each other to the extent that the other is pushed away. Like two piglets fighting over the same teet. The phenomenon suggest that the flux attracted to each magnet is so great that it can be considered at maximum flooded capacity. You are pointing two one-way fire hoses toward each other and the pressure is too great to force them completely together. Think about your question in those terms. A magnet is a one way street. And a closed core transformer virtually transforms the primary winding back into magnetic energy whence it originally came at the power station, and the secondary winding then virtually transforms the new magnetic energy back into electrical energy. Because no transfer is perfect, you will never get a larger electrical flow out of a transformer or any metal than what goes in. Magnetic power and electrical power are exactly the same in strength. Our limitations simply force us to measure them differently.

Answer 2

Well, your question is about iron (Fe), so you are talking about a specific material, consequently my answer won't be general. Iron is ferromagnetic and it is a conductor.

• Ferromagnetism: it is due, roughly speaking, to the alignment of internal magnetic dipoles in the direction of the external magnetic field, as you said. The magnetic field inside ($\bf{B}$) grows linearly with the external field $\bf{H}$, provided the latter is small: $\bf{B} = \mu_0 \kappa \bf{H} = \mu_r \bf{H}$.
• Conductor: a remarkable feature of a (perfect) conductor at equilibrium is the fact that the electric field inside vanishes. So the field is not reduced by $\varepsilon_r$ as you said, or if you prefer, it is but $\varepsilon_r\to\infty$.