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Q give rise to D => E => V => I => H.

  1. Jun 5, 2014 #1
    Charge is the most fundamental quantity.

    consider a point charge Q to simplify our mental picture:
    Q will give rise to a Immutable D, whatever material that Q was placed in.

    E will then = D/ε. Stronger dielectric material will really weaken you E here. However this is not a contradiction to how capacitor works.

    if you integrate E along some path connecting 2 points, you will get the potential difference between those 2 points.

    SURE, you can artificially fix E and claim D will vary in different material. to me, it is a misunderstanding how the physical world behaves.

    I => H or B is muddy in my head.
    In a coil: Does dv/dt drives ø directly or does V drives I and NI drives ø and that ø will reversibly affect I (with saturation, who drives whom matters) ?
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  3. Jun 5, 2014 #2

    Simon Bridge

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    It is certainly a fundamental thingy - but there are more fundamental ones depending on who you ask.

    Unfortunately Nature does not care about what things are like to each of us. Nature just is.

    Consider: can photons exist without charges?

    Another formulation of electromagnetism is in terms of potentials... the charge can still give rise to a potential via Poisson's equation: $$\epsilon \nabla^2\phi = -\rho_{free}$$ ... then the potential gives rise to the fields.

    The relationships between E D and whatever are not cause and effect.
    One does not drive the other. They are just relationships.

    Currents are moving charges.
    So you can get things back to you favorite fundamental.

    Either or both depending on the exact setup.

    The current is to magnetism what charge is to electricity.
    However, the subject is best understood as unified electromagnetism - all together.
    Look up "Maxwel's equations".
  4. Jun 5, 2014 #3


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    I am not sure what u mean by the symbol of the empty set (what it appears to me via internet explorer browsing when u say dv/dt drives it), but i guess u mean the magnetic flux. In the case of a coil connected to a voltage source V, V gives rise to current I, which creates a time varying magnetic field B which in turn will create a time varying non conservative electric field D1 which will affect the original current I.
  5. Jun 5, 2014 #4
    Thank you very much for your replies, I think I am getting somewhere.

    first, I think the ϵ∇2ϕ=−ρfree example actually reinforced my mental picture. the intention of that equation is: I have a potential field, I wonder what's underlying cause of it? and the answer is: density of charges. and you can see, that potential is plagued by the MATERIAL ϵ it is in. Potential, despite of its noble qualities, still bears in its bodily frame the indelible mark of it lowly origin.

    That "Currents are moving Charges" was my biggest temptation, along with M dipoles and quantum spin, to think that charges are the fundamental driving force of the Magnetic world. But the rate of flow does not meaningfully translate into the speed of movement of charges, so I am not quite sure.

    Why am I so obsessed with this heretic idea of "Fundamental"? it is exactly because of this question: " WHo is exciting the coil to produce flux?" The Voltage across the coil or the Current flowing in the coil?

    according to Mr Bridge and Delta2, and my personal belief, it should be the current. But if that's the case, then why so many text books just maddeningly assume a Sin V will get a PERFECTLY shaped Sin Flux (considering saturation and hysterisis) ?

  6. Jun 6, 2014 #5


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    D is not very fundamental, on a microscopic level, it is sufficient to consider E. Also note that even in material media, Q fixes only the longitudinal part of D while the transversal part depends on boundary conditions and the like.
  7. Jun 6, 2014 #6

    Simon Bridge

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    Or you could ask how that charge density go there if not in response to the potential?

    The intention of the equation is to show a relationship - not cause and effect.
    How you look at it depends on the question you want to ask.

    Sure it does.
    If n charges per unit volume of magnitude e move with a drift velocity of v through a cross-section area A, then the current is I=neAv.

    So currents are moving charges - but what are they moving with respect to?
    Why - with respect to the ammeter of course!
    If the ammeter was moving along with the charges, then there would be no current and no magnetic field - only the electric field from the charges remains.

    The person turning the dial is causing the changes. If the dial controls voltage, then the voltage causes everything, if the dial controls the current, then the current controls everything. It just depends on how the equipment is rigged up.

    Because they are not taking into account hysteresis or saturation.

    An EM field can propagate through space all by itself even if the charges that originated it have vanished. It consists of self consistent E and B fields where the E field induces a B field which is just the right shape to induce the original E field ... but it's chicken-and-egg time: the same description works if you start with the B field.

    All this is classical.
    Go to Relativity and your idea that charges are behind everything looks better.
    At the quantum level though, we get a picture where there are intrinsic magnets: no current.
    Electromagnetism is understood in terms of interactions with photons.

    Now photons are quanta of the EM field - and charges are then understood in terms of their interactions ... thus the field gives rise to the charge??

    More generally, particles are understood in QFT as disturbences in an underlying Field - so the Field gives rise to the particles.

    I'm not trying to convince you of anything - I'm just trying to show you that what causes what is not so straight forward. At the level you are trying to understand these things, you should not be thinking that the equations imply one side of the equals sign is any more fundamental than the other.
    Last edited: Jun 6, 2014
  8. Jun 6, 2014 #7


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    Mathematical relations like [itex]V=-\dfrac {d\phi}{dt}[/itex] dont necessarily give u the full picture of the underlying physical reality. Even in classical mechanics where u have for a rigid body [itex]F_{net}=ma_{com}[/itex] this equation tell u nothing about the internal forces in the rigid body which in the general case are the ones responsible for accelerating the c.o.m of the body.
  9. Jun 6, 2014 #8
    V=−dϕ/dt is perfectly acceptable to me, as it is the 3rd maxwell equation.
    and I will let go of the "fundamental" stuff.

    let's just focus on the magnetization graph I posted above. Why is sin wave voltage across a coil inducing a perfect sin wave flux? shouldn't both current and flux be skewed by the hysterisis and saturation? I don't think this is how the 4th maxwell equation is applied. And I don't think the 3rd equation can be reversed either
  10. Jun 6, 2014 #9

    Simon Bridge

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    There is no way of knowing from the graph alone - where did you get it from?

    I note that there are three curves, only one looks like a good sine wave... that is labelled with a phi.
    Probably flux. The other two are V (a voltage maybe) and and iexC (some sort of current). These don't look like nice sine waves at all - though the V curve is sort-of sinusoidal.

    I would guess that the flux was applied and the other two curves are calculated from that, taking into account... pretty much whatever the author wanted to.
  11. Jun 7, 2014 #10


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    Ok i think i understand you now. I think the confusion is between the concepts of voltage drop and that of the emf of the coil. It's the emf of the coil that will always be -dϕ/dt, however the voltage drop across the coil is affected by other things for example the ohmic resistance of the coil (so in that case it will be V=IR-dϕ/dt). So even if the voltage drop V across a coil is perfect sinusoidal due to a source voltage applied there, the term dϕ/dt can be different.
  12. Jun 7, 2014 #11


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    An EMF is not a potential. To the contrary it is related to the curl of the electric field according to the Maxwell equation (Faraday's Law)
    [tex]\vec{\nabla} \times \vec{E}=-\frac{1}{c} \frac{\partial \vec{B}}{\partial t}.[/tex]
    The integral form is often not given correctly. It reads
    [tex]\text{EMF}=\int_{\partial A} \mathrm{d} \vec{x} \cdot \left (\vec{E}+\frac{\vec{v}}{c} \times \vec{B} \right )=-\frac{\mathrm{d}}{\mathrm{d} t} \frac{1}{c} \int_A \mathrm{d}^2 \vec{F} \cdot \vec{B}.[/tex]
    For the derivation, see the Wikipedia:

  13. Jun 7, 2014 #12
    I really really appreciate all of your time and effort to understand my concern and answering. This is brilliant.

    My bad for not structuring my scenario clear, so here is the whole setup:

    the circuit is simply a SinWave voltage source (ideal) connected to a single coil with an closed iron core inside. It would like the picture below while ignore the labels.

    Only consider saturation and hysteresis of the core and assuming no resistance and no eddie current of core loss or leakage. the relation between the voltage of the source, the current in the coils and the flux will look like this:

    SO many text books just say:" Farady said v = dø/dt, so if v is sin(something) then ø is cos(something), right there, and done". I was like WTF, that's the induced voltage from a driving flux. Flux has nothing to do with voltage. flux is the result of current: line integral H*L = i. the E inside Maxwell's 4th equation in this case means the E inside of the wires. and H it generated around the winding... OK...that apparently does imply a relationship of V_magnetizing = d( flux_result ) / dt... I just confused myself. I thought 4th equation does not apply here, but apparently it does apply inside the winding wires.

    but... what about the current side of the story, the current flowing in the wires, that will get some H going around the winding wires as well.

    Some one please help me to apply maxwell 4th equation in this scenario.
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