- #1
tim9000
- 867
- 17
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
ΦB = B*Area
&
D = εE
ΦE = 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 = ρfree ?
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
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
ΦB = B*Area
&
D = εE
ΦE = 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 = ρfree ?
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