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Let us suppose that there is a block of a ferromagnetic material inside a very long ideal solenoid, the magnetic field lines inside are in a straight line perpendicular to the surface of the block at both the ends.Why does the magnetic field inside the block increases? It is known form the boundary conditions of magnetic fields that the perpendicular or the normal component of the magnetic field $\vec{B}$ doesn't change when it goes from one medium to other.So, what's happening here?

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  • $\begingroup$ While the normal component of the B field is continuous (and not that of the H field), the tangential component of H field is continuous. Both have to be taken into account. $\endgroup$
    – hyportnex
    Jul 7, 2020 at 16:31

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The field from the solenoid would cause an alignment of the atomic magnetic dipoles within the ferromagnetic material. This would be equivalent to putting a bar magnet inside the solenoid. The resultant field would be the vector sum of the two at each point. The field would not change immediately upon leaving the end of the bar, but the contribution from the bar would start to spread (and curve back around to the other end). At some distance from the bar the field of the solenoid would predominate.

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  • $\begingroup$ So the concept that is studied that tells that the normal component of the magnetic field is continuous? Its talking about which media? Also why is the magnetic field inside the ferromagnetic material is equal to the magnetic susceptibility times the outside (solenoid) magnetic field? $\endgroup$
    – shahrOZe
    Jul 7, 2020 at 15:37
  • $\begingroup$ In this case, the field is continuous from inside the ferro-magnet to just outside. The susceptibility is defined as the ratio of the resultant field to the applied field. $\endgroup$
    – R.W. Bird
    Jul 7, 2020 at 15:44

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