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In the course of my learning electromagnetism, I’ve noticed there are a striking amount of symmetries in electrostatics and magnetostatics, almost down to replacing divergence operators with curl operators. For instance,

$$\vec P = \epsilon \vec E$$ $$\vec H = \mu \vec B$$

For linear media, and

$$\vec D = \epsilon_0 \vec E + \vec P$$ $$\vec B = \mu_0 (\vec H + \vec M)$$

And where $\vec H$ is defined, at least in Griffiths, in a completely analogous way to electric displacement, save for the typical curl operator that is usual for magnetostatics and a current density instead of charge density.

I am tempted to say that the effects of polarization and magnetization are totally analogous, that “$\vec H$ is basically the magnetostatic equivalent of $\vec D$” since I have far more trouble visualizing magnetization than I do polarization so if I can get away with thinking this way it’d make my learning easier I think. Do I have it wrong? Am I justified in thinking things in terms of analogizing from polarization? Am I oversimplifying things massively? Be as pedantic as you’d like.

sangstar
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1 Answers1

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$\vec{H}$ is basically the magnetostatic equivalent of $\vec{D}$” since I have far more trouble visualizing magnetization than I do polarization so if I can get away with thinking this way it’d make my learning easier I think. Do I have it wrong?

All these analogies are limited and context-dependent.

Sometimes $\mathbf H$ is analogous to $\mathbf E$, since in static scenario they both obey Coulomb's law, have similar equations, similar "lines of force"; bar magnet' H field is similar to electrically polarized bar's E field.

But sometimes $\mathbf B$ is analogous to $\mathbf E$, for example in diamagnetics (copper, bismuth), the magnetized medium decreases $\mathbf B$ field inside, just as polarized dielectric decreases $\mathbf E$ inside.

There is no generally valid analogy, these are 4 different quantities with unique properties.

Ján Lalinský
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