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Now, my question is, wouldn't it make more sense to say B is the analog to E? Because E and B are more fundamental in the sense that they are the fields you can actually measure by placing a charge in an electric field or a current in a magnetic field and measure the resulting force independently of the medium. With the Lorentz force law: [itex]\vec{F} = q\left(\vec{E} + \vec{v} \times \vec{B}\right)[/itex].

On the other hand, D and H occur from Gauss's law and Ampere's law respectively, and are indirect results of charge distributions and current distributions, and cannot be "measured" directly. The surface integral of D over a closed surface is the total enclosed charge in the surface, and the line integral of H around a closed loop is the total current crossing the loop. So D and H are both related to charge density and current density.

In fact, I think B should have been called the magnetic field, and H the magnetic flux density.

Are there any arguments for choosing to call H the magnetic field and B the magnetic flux density?