Understanding Gauss' law: diff b/w E and D flux?

[tim9000]

I noticed the other day something odd in how we use Electric and Magnetic flux.
The definitions I refer to are magnetic flux density (B), magnetic flux intensity (H), electric displacement field (D) or Electric field density (D) and electric field (E):
B = μH
Φ_B = B*Area

&

D = εE
Φ_E = E*Area

for magnetic and electric fields, respectively.

Is the electric displacement field the same thing as electric field density?

So this seems like a lack of symmetry of the flux quantities at first glance as the magnetic field flux is based off a magnetic field density but electric flux is based off electric field intensity. I find this odd, is there a reason for this/why do we do it this way?

My other question is along the same lines but regarding Gauss' law:

According to wiki:
"Equation involving the E field
Gauss's law can be stated using either the electric field E or the electric displacement field D. This section shows some of the forms with E; the form with D is below, as are other forms with E."

Site:
https://en.wikipedia.org/wiki/Gauss'_law

It further says:
"Equation involving the D field
Free, bound, and total charge
Main article: Electric polarization
The electric charge that arises in the simplest textbook situations would be classified as "free charge"..."

I also tried reading:

https://en.wikipedia.org/wiki/Electric_displacement_field

&

https://en.wikipedia.org/wiki/Electric_displacement_field

Which states:
"The displacement field satisfies Gauss's law in a dielectric:

∇ ⋅ D = ρ − ρ b = ρ f

.
Proof:
[show]
"

But I'm confused, is Maxwell's differential equation of Gauss' law
(https://wikimedia.org/api/rest_v1/media/math/render/svg/ff0076e721a4b485bda8ff427f00e73c6efb6006)
the total charge density (both bound and free charge) and why is it not the same as ∇⋅D = ρ_free ?
Basically, what's the difference between and why do we use one and not the other?
I'm struggling to get this intuitively.

Much appreciate your assistance.

Cheers

 

[Charles Link]

I think the answer to your question is somewhat simple, but it took me lots and lots of effort to figure this out. Both the quantities $D$ and $H$ are non-physical, unlike $E$ and $B$. The parameters $D$ and $H$ can not be measured. They are very useful mathematical constructions, but don't represent real physical entities. For a lot of detailed mathematics where I was able to tie the "pole method" of magnetism to the "surface current" method, see https://www.overleaf.com/read/kdhnbkpypxfk Because the "pole model" of electrostatics also enters into the discussion, I believe I also discussed in the write-up how $D$ like $H$ is also simply a mathematical construction. $\\$ Additional item of interest: For the electric field $E$, we have, in c.g.s. units, $\nabla \cdot E=4 \pi \rho_{total}$ where $\rho_{total}=\rho_{free}+\rho_{p}$. It is impossible for any physical device to distinguish the electric field $E$ that comes from $\rho_{free}$ vs. that which comes from $\rho_p$. Thereby $D$, which distinguishes the two with the equation $\nabla \cdot D=4 \pi \rho_{free}$, is non-physical, and simply a mathematical construction. (Note: Polarization charge density comes from gradients in the polarization vector $P$. $\rho_p=-\nabla \cdot P$). $\\$ Editing: And similarly for the magnetic field $B$: The $B$ field caused by currents in conductors can not be physically distinguished from that caused by bound magnetic surface currents. The magnetic pole method does a mathematical construction that generates a well-defined $H$, but it is non-physical, and the magnetic field that is measured in all cases is the $B$ field.