[hamdani yusuf (OP)]

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

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?

[paul cotter]

∇xH=J

[hamdani yusuf (OP)]

∇xH=J

How can you use this formula to answer my questions?

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?

[hamdani yusuf (OP)]

So you have disproved Ohm's law. Amazing.

Let's have a common understanding first.

Impedance Explained.

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 Triangle

Symbols
--------------
R = Resistance, measured in Ohms
Z = Impedance, measured in Ohms
X = Reactance, measured in Ohms
C = Capacitance, measured in Farads
L = Inductance, measured in Henrys
Xc = Capacitive Reactance, measured in Ohms
XL = Inductive Reactance, measured in Ohms

Interestingly, the dimension of those measurements all involve mass.

[paul cotter]

∇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.

[hamdani yusuf (OP)]

∇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.

This formula doesn't seem to distinguish between electron current and ionic current.
What's the current density of a proton moving at velocity v in a lab frame of reference?

[hamdani yusuf (OP)]

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

Maxwell's equations still need two empirical constants, electric permittivity and magnetic permeability of vacuum. In a medium, those constants must be replaced by the permittivity and permeability of the medium.
Maxwell's equations don't explain how the presence of material particles affect those constants.
https://en.wikipedia.org/wiki/Permittivity
https://en.wikipedia.org/wiki/Permeability_(electromagnetism)

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

[alancalverd]

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

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

 

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

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

[hamdani yusuf (OP)]

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

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.
Are these cases equivalent?
Do you consider theory of relativity, which says that magnetic field in one reference frame becomes electric field in other reference frame?

[paul cotter]

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".

[hamdani yusuf (OP)]

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

Consider the following case. An aluminum sheet 100x100x1 mm is laying on the floor inside a vacuum chamber. Another identical plate is positioned parallel to the first 1 meter above it. The electric and magnetic field of a point right at mid point between those plates can be calculated using ε0 and μ0. But if the distance between them is reduced to just 1 nm, you need to use different ε and μ for most practical purposes.
Another example is in the space inside a metamaterial. For a range of frequency, its ε and μ are significantly different from air. Ordinary dielectric media like water and glass can be modeled as metamaterial with extremely small structures.
Another example is inside a waveguide of microwave radar.

[hamdani yusuf (OP)]

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".

Do you think these 3 cases produce identical 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.

[paul cotter]

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.

[alancalverd]

But 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.

[Bored chemist]

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

Why?

[paul cotter]

The question as to the "source of the magnetic field" has been comprehensively addressed. This thread is becoming "an essay in confusion, too long to read".

[hamdani yusuf (OP)]

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.

Make the electrons in the wire move to the left at v relative to the wire, then move the current carrying wire to the right at v. This makes the electrons stationary in the lab frame, while the protons move to the right at velocity v.

Perhaps 17 pages weren't enough to describe the problem so clearly that everyone can understand. But at least you have now realized that three cases above are not identical.

[hamdani yusuf (OP)]

But 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 equations don't cover those other phenomena in details. That's why they need empirical fudge factors like permittivity and permeability to address those other phenomena in a broad brushstroke.

[paul cotter]

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.

[hamdani yusuf (OP)]

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.

What's the permittivity and permeability of space between two water molecules in the center of an ice block at 1 atm and 0 centigrade?
How does iron core affect magnetic field around a current carrying solenoid?