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Students commonly wonder about the near-analogies between electricity & magnetism. One in particular:

Polarization $\mathbf{P}$ and magnetization $\mathbf{M}$ are the infinitesimal densities of electric and magnetic dipole moments ($\mathbf P = {\mathrm d\mathbf p \over \mathrm d V}$ and $\mathbf M = {\mathrm d\mathbf m \over \mathrm d V}$). Flux lines exit the positive end of electric and magnetic dipole vectors the same. Yet $\mathbf{P}$ and $\mathbf{M}$ have the opposite effect on the total (= fundamental = free + bound charge) fields $\mathbf{E}$ and $\mathbf{B}$. Why is the $E$-field lessened by parallel electric dipoles, while the $B$-field is greater when it induces parallel magnetic dipoles?

Qmechanic
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alexchandel
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1 Answers1

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Because you chose the pair $\mathbf E,\mathbf B$ instead of the pair $\mathbf E,\mathbf H$ and because you assume magnetically paramagnetic or ferromagnetic medium.

If the medium is diamagnetic (copper, bismuth), then its magnetization due to external field decreases $\mathbf B$ inside.

If you want to talk about iron or steel, those are ferromagnetic, external field induced magnetization increases field $\mathbf B$ inside. But it decreases field $\mathbf H$ inside.

So there is no general relation/analogy, the relation between external magnetic field $\mathbf B_{ext}$ and medium-induced field $\mathbf B_{ind}$ depends on the kind of material medium.

Ján Lalinský
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