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

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)

• 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 $$\varepsilon_r\to\infty$$.
• So u mean Total B(inside) = $u_r$ B(outside)? Jun 30, 2020 at 20:21
• Not exactly, more precisely $\bf{H}$ is the magnetic field produced by an external source, but computed inside the material, while $\bf{B}$ is the magnetic field produced by all the sources (including Ampère currents in the material) computed inside the material. Jul 1, 2020 at 7:40