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and the magnetic field around a current-carrying conductor isn't anything to do with the sum of carrier spins, which is zero.

∇xH=J

Where does the magnetic field around a current-carrying conductor come from?What would happen if the conductor is replaced by a conductive salt solution inside a hose?

So you have disproved Ohm's law. Amazing.

In this video I compare similarities from the physical world that you can see and touch, to help share how I think about Impedance. You will learn about ?Opposing? forces called ?Reactance? and how these, together with ?Resistance? combine to form what we call ?Impedance?. Whilst I do go through some formulas, these are not the key intended purpose of the video. For many people, the formulas are not really important. What is more important, is to be able to visualise in your mind exactly what is going on with AC circuits and to imagine that in a way that makes sense to you.I hope the analogies I share, which I have picked up from others over the years, really help your thinking as much as it has me.Topics Covered-------------------------- Resistance- Impedance and opposition to current flow- Capacitors- Capacitive Reactance- Inductors- Inductive Reactance- Impedance TriangleSymbols--------------R = Resistance, measured in OhmsZ = Impedance, measured in OhmsX = Reactance, measured in OhmsC = Capacitance, measured in FaradsL = Inductance, measured in HenrysXc = Capacitive Reactance, measured in OhmsXL = Inductive Reactance, measured in Ohms

∇xH=J, the circulation of the magnetic field equals the current density. Or alternately the closed line integral of the magnetic field around a circumference enclosing the conductor equals the current. If you can't calculate from these basics you are out of your depth.

https://en.wikipedia.org/wiki/Maxwell%27s_equationsIn partial differential equation form and SI units, Maxwell's microscopic equations can be written as

What's the current density of a proton moving at velocity v in a lab frame of reference?

I guess applying Maxwell's equations on microscopic level fails due to this discrepancy.

same as that of an electron moving at the same speed in the opposite direction. i = dq/dt, and qe = - qp

No. The values of ε and μ are just normalising constants that relate electric and magnetic phenomena to common (nowadays SI) units.

Of course we take relativity into account. There is only one field, the electromagnetic field which depending on one's reference frame may appear to be an electric field, a magnetic field or both. If you understood this there was no need for 17 pages of discussion on the "origin of the magnetic field".

Consider following situations.A. In a long straight wire, its protons move to the right with speed v.B. The electrons move to the left with speed v.C. protons move to the right with speed v/2 while the electrons move to the left with speed v/2.

But if the distance between them is reduced to just 1 nm, you need to use different ε and μ for most practical purposes.

How can we have protons moving in a wire?, that does not make sense unless the wire is a tube full of ionised hydrogen in which the analysis would be extremely complicated. Again I say the answer to the "origin of the magnetic field" has been answered by relativity.

Quote from: hamdani yusuf on 03/07/2024 22:44:02But if the distance between them is reduced to just 1 nm, you need to use different ε and μ for most practical purposes.No, the same values apply but other phenomena become more (field emission) or less (fringe fields) significant when the distance changes, so the effective value of capacitance, say, deviates from the ideal infinite parallel plate calculation. The trick is to add a "guard plate" so the lines of the measured field remain parallel.

Maxwell's equation deal with simple symmetric topologies, if you explore any other conditions you have add minor alterations. This does not in any way impugn these equations. Permittivity and permeability are most definitely NOT fudge factors, they are fundamental properties of space. You are going round in circles like a dog chasing it's tail, and not learning anything.