Elecric Flux, Vm or Q

Magnetic Flux (symbol Φ) is used as in the following equation.

            dΦ
v(t)  = ------
             dt

By using analogy Electric Flux can be considered as Electric Charge (symbol Q ) as in the following equation.

             dQ
i(t)  =  ------
             dt

I find this definition in my old Penguin's Electronics dictionary and Physics dictionary.

However, an official definition seems as follows:

From wiki

"
In electromagnetism, electric flux is the measure of flow of the electric field through a given area. Electric flux is proportional to the number of electric field lines going through a normally perpendicular surface. If the electric field is uniform, the electric flux passing through a surface of vector area S is

${\displaystyle \Phi _{E}=\mathbf {E} \cdot \mathbf {S} =ES\cos \theta ,}$

where E is the electric field (having units of V/m), E is its magnitude, S is the area of the surface, and θ is the angle between the electric field lines and the normal (perpendicular) to S.
For a non-uniform electric field, the electric flux dΦ_E through a small surface area dS is given by

${\displaystyle d\Phi _{E}=\mathbf {E} \cdot d\mathbf {S} }$

(the electric field, E, multiplied by the component of area perpendicular to the field). The electric flux over a surface S is therefore given by the surface integral:

${\displaystyle \Phi _{E}=\iint _{S}\mathbf {E} \cdot d\mathbf {S} }$

where E is the electric field and dS is a differential area on the closed surface.

"

The point is ＜electric flux is the measure of flow of the electric field through a given area＞. Magnetic flux is, however, not the measure of flow of the magnetic fields (H, B) through a given area, but simply Φ.

The unit of Electric filed is V/m. Therefore unit wise

E.dS is (V/m) x m² so in ＜Vm＞. ＜Vm＞may have a meaning itself like ＜Im＞. For instance,

                      dΦ               
＜Vm＞ is   ------ x m.
                      dt                      
                                           dm
Can we change this to  Φ x ------  = Φv (v = velocity) ?
                                            dt

This can be considered as a velocity of Φ or Φ is moving with velocity, but difficult to imagine.

 Likewise on the otherhand

                     dq               
＜Im＞ is   ------ x m.
                      dt                      
                                            dm
Can we change this to  q x ------  = qv (v = velocity) ?
                                            dt

This can be considered as a velocity of q or q is moving with velocity and usually considered in Electric Field creating Force. Lorentz Force.

From Wiki

"
Lorentz force, the force exerted on a charged particle q moving with velocity v through an electric E and magnetic field B. The entire electromagnetic force F on the charged particle is called the Lorentz force (after the Dutch physicist Hendrik A. Lorentz) and is given by F = qE + qv × B
"


Wiki explains ＜im (Ampere-meter, A-m)＞by quoting Einstein as follows:

"

Derivation

Einstein proved that a magnetic field is the relativistic part of an electric field. This means that while an electric field acts between charges, a magnetic field acts between moving charges (as a charge moves through space more quickly and through time more slowly, its electromagnetic force becomes more magnetic and less electric). Therefore, the pole strength is the product of charge and velocity.
${\displaystyle 1~\mathrm {A\cdot m} =1~\mathrm {C} \cdot {\frac {\mathrm {m} }{\mathrm {s} }}}$

Usefulness

Few calculations actually involve the strength of a pole in ampere-meters because a single magnetic pole has never been isolated. Magnets are dipoles which require more complicated calculations than monopoles. However, the strength of a magnetic field is measured in teslas and one tesla is one newton per ampere-meter which confirms that the unit for pole strength is indeed the ampere-meter.


" a charge moves through space more quickly and through time more slowly "

This part is a bit difficult to understand.

" Therefore, the pole strength is the product of charge and velocity."

 Why " therefore " ?  Some explanation is needed.

"
the strength of a magnetic field is measured in teslas and one tesla is one newton per ampere-meter which confirms that the unit for pole strength is indeed the ampere-meter.
"

Here "the strength of a magnetic field" is B (also called "magnetic flux density"). This part is clear unit wise.

Anyway ＜im＞seems to be <magnetic pole strength>. But when differentiate this ＜im＞with time, ＜q＞and ＜v (velocity) ＞come out.  This transformation (after differentiating with time) is interesting.  We can apply this to ＜vm＞, which is already shown above.  When differentiate this ＜vm＞with time, ＜Φ＞and ＜v (velocity) ＞come out.

                      dΦ               
＜Vm＞ is   ------ x m.
                      dt                      
                                       dm
We can change this Φ x ------  = Φv (v = velocity)
                                        dt


H (field) is in I/m while E (field) is in V/m. H.dS is therefore in ＜Im＞.

μ0  H (I/m) = B (Φ/m² ) - Magnetic flux density

ε0 E (V/m) = D (Q/m² ) - Electric flux density. Name wise, Q is Electric flux.  D is also called Displacement and D is for Displacement.

These are very symmetrical and the names represent the meaning as compared with ＜electric flux is the measure of flow of the electric field (V/m) through a given area＞. We can visualize it as a bundle of V/m lines while it is difficult to visualize H field (I/m) as a bundle of I/m lines though not impossible if you are familiar with the relation with I (or rather di/dt) and L or μ0  (L = mμ0).

                di(t)
v(t)  = L ------
                 dt

This ＜v(t)＞ generally changes with time as ＜i(t)＞ changes with time.  When＜i(t)＞ does not change with time (being constant), v(t) = 0.

            dΦ
v(t)  = ------
             dt

Combining we get

                di(t)       dΦ
v(t)  = L ------  = ------
                 dt          dt


Therefore

Ldi(t) = dΦ

Li =  Φ

i =  Φ / L =  Φ / mμ0

Here we can find the relation between the original＜i(t)＞ and Φ . 

＜i(t)＞ is  proportionally caused by Φ (Magnetic Flux, Im) with 1/L or inversely proportionally caused by L. In other words

L being fixed, ＜i(t)＞ becomes larger as Φ becomes stronger.

Φ being fixed, ＜i(t)＞ is needed less as L becomes larger to keep this fixed Φ.

 
The definition of Φ (Weber) is


From wiki

"
A change in flux of one weber per second will induce an electromotive force of one volt (produce an electric potential difference of one volt across two open-circuited terminals).

Officially,
Weber (unit of magnetic flux) — The weber is the magnetic flux that, linking a circuit of one turn, would produce in it an electromotive force of 1 volt if it were reduced to zero at a uniform rate in 1 second.

"

which means
       
0v -->  1v  x 1 sec =1 --> 0 Weber
        
but more generally


                dΦ
v(t)  = -  ------
                 dt

(Added the minus sign)



＜Vm＞ x ＜Im＞ = VIm². VI is Electric Power.

＜Φv＞ x ＜qv＞ (v = velocity) = Φqv².

E x H (cross product) is called "Poynting vector". Unit wise = (V/m) x (I/m) = VI/m²

From wiki

"
Poynting vector represents the directional energy flux density (the rate of energy transfer per unit area) of an electromagnetic field. The SI unit of the Poynting vector is the watt per square metre (W/m²).

"

Watt is not Energy but Electrical Power - the rate of energy transfer per time.

sptt