Two questions regarding electromagnetism

[CaveDave]

These are two questions I have recently wondered about:

1) Premise: Magnetic fields cause moving charges to curve according to the polarities present and the relative directions and velocities of motion.

Setup: One sets up an assembly of a powerful, variable electromagnet and a cylinder of electrically conducting material(*), with an aspect of, say, a 1" diameter by 1" length cylinder with collecting electrodes on each circular face (connecting to an external current/voltage sourcing/measurement system) and aligned to the magnet's pole faces along the axis of the centers of the circular faces.
[* - this might be in any physical state: solid, liquid, gas, or plasma]

Question: As the field is "dialed" up, I would assume that the current carriers would slowly deviate from purely axial to increasingly helical; would the lengthening of the path taken cause the resistance (voltage vs current) to increase, and could this be used to measure field strength (or is this just some variant of something simple like the Hall Effect)?



2) Premise: I have read that superconductors "expel" magnetic lines-of-force: I presume this is because a "line" attempting to cut the material generates a counter EMF and this forces the line to keep it's distance.

Setup: A slug of room-temperature type material above it's superconducting range is placed in a strong magnetic field, and then cooled to below that temp. radially inward perpendicularly to the excitation field lines.

Question: Will the field be expelled when the core reaches S.C., will the field be "frozen in", making a "permanent" magnet, or will something else altogether occur?



Just curious if anyone knows.

Cheers,

Dave

 

[Dilb]

These are two questions I have recently wondered about:

1) Premise: Magnetic fields cause moving charges to curve according to the polarities present and the relative directions and velocities of motion.

Setup: One sets up an assembly of a powerful, variable electromagnet and a cylinder of electrically conducting material(*), with an aspect of, say, a 1" diameter by 1" length cylinder with collecting electrodes on each circular face (connecting to an external current/voltage sourcing/measurement system) and aligned to the magnet's pole faces along the axis of the centers of the circular faces.
[* - this might be in any physical state: solid, liquid, gas, or plasma]

Question: As the field is "dialed" up, I would assume that the current carriers would slowly deviate from purely axial to increasingly helical; would the lengthening of the path taken cause the resistance (voltage vs current) to increase, and could this be used to measure field strength (or is this just some variant of something simple like the Hall Effect)?

I'm not quite sure where the magnetic field would be pointing. It the magnetic field is in the direction of the current, then in a plasma, for example, the charge carriers would start moving in little helices, rather than bouncing around randomly side-to-side. Since the net current has no net force on it, I'd expect there's very little change in resistance. It wasn't something I was worried about when I did resistance measurements in a 4 Tesla field.

If the field is perpendicular to the current, then you produce the hall effect. The resistance would slightly increase, as the current is being 'pushed' into a slightly smaller region, but that's still pretty small, at least classically. The quantum hall effect may change that, but I've never looked at the particulars.

2) Premise: I have read that superconductors "expel" magnetic lines-of-force: I presume this is because a "line" attempting to cut the material generates a counter EMF and this forces the line to keep it's distance.

Setup: A slug of room-temperature type material above it's superconducting range is placed in a strong magnetic field, and then cooled to below that temp. radially inward perpendicularly to the excitation field lines.

Question: Will the field be expelled when the core reaches S.C., will the field be "frozen in", making a "permanent" magnet, or will something else altogether occur?



Just curious if anyone knows.

Cheers,

Dave

That's actually the big difference between perfect conductors and superconductors. A perfect conductor would freeze the field lines in, but superconductors actually expel the magnetic lines.

Even regular conductors react to changing magnetic fields to try and minimize them, that's Lenz's law. A perfect conductor would succeed at minimizing the field, while superconductors reduce it to zero spontaneously.

 

[CaveDave]

I'm not quite sure where the magnetic field would be pointing. It the magnetic field is in the direction of the current, then in a plasma, for example, the charge carriers would start moving in little helices, rather than bouncing around randomly side-to-side. Since the net current has no net force on it, I'd expect there's very little change in resistance. It wasn't something I was worried about when I did resistance measurements in a 4 Tesla field.

I tried to indicate that the bulk current and magnetic field were parallel and coaxial, but I may not have worded it well.

Your first guess was correct. You seem to be saying that as the helices become increasingly "tight" (as the field increases), therefore lengthening their effective path, that the effect will be negligible. Interesting.

If the field is perpendicular to the current, then you produce the hall effect. The resistance would slightly increase, as the current is being 'pushed' into a slightly smaller region, but that's still pretty small, at least classically. The quantum hall effect may change that, but I've never looked at the particulars.

Would the hall effect not come into play as the helix angle approached perpendicular at extremely high fields?

That's actually the big difference between perfect conductors and superconductors. A perfect conductor would freeze the field lines in, but superconductors actually expel the magnetic lines.

Even regular conductors react to changing magnetic fields to try and minimize them, that's Lenz's law. A perfect conductor would succeed at minimizing the field, while superconductors reduce it to zero spontaneously.

Somehow, I located a link to Hyperphysics (someone here must have provided it long ago and I had it bookmarked) where I found that fact in the "superconductors" article, but I am not sure I understand why it is that way.

Cheers,

Dave

 

[Dilb]

I tried to indicate that the bulk current and magnetic field were parallel and coaxial, but I may not have worded it well.

Your first guess was correct. You seem to be saying that as the helices become increasingly "tight" (as the field increases), therefore lengthening their effective path, that the effect will be negligible. Interesting.

Would the hall effect not come into play as the helix angle approached perpendicular at extremely high fields?

There's no reason for the path length to increase: the magnetic field doesn't do any work on a charge carrier, so the perpendicular velocity stays the same relative to the longitudinal velocity. The most the magnetic field could do is cause the charge carriers to radiate off their perpendicular velocity, until it reaches the ground state, whether we treat the ground state as a straight line or a Landau level.

The hall effect comes in when there's a net force across the entire conductor shoving charges to one side. If the charges are moving in helices, then they don't move to any particular side, and you don't get any Hall effect.

Somehow, I located a link to Hyperphysics (someone here must have provided it long ago and I had it bookmarked) where I found that fact in the "superconductors" article, but I am not sure I understand why it is that way.

Cheers,

Dave

If you'd like a neat semi-classical sort of reasoning, I'm fresh out. Superconductors are complicated quantum systems, and they respond to magnetic fields by expelling them. I don't think there is a particularly compelling argument from the BCS equations, at least not yet.

 

[sol invictus]

Question: Will the field be expelled when the core reaches S.C., will the field be "frozen in", making a "permanent" magnet, or will something else altogether occur?

That depends on the type of superconductor and the strength of the field.

A type I SC will either expel the field entirely or fail to reach the SC state even after the temperature is lowered below the zero field transition point (that will happen in the field is sufficiently strong).

A type II SC will either concentrate the magnetic flux into separate vortices, each carrying one unit of magnetic flux, or if the field is too strong will fail to reach the SC state at all. The former case isn't a permanent magnet, though - the vortices (field lines) can move around, although they tend to repel each other.

 

[Ziggurat]

If you'd like a neat semi-classical sort of reasoning, I'm fresh out. Superconductors are complicated quantum systems, and they respond to magnetic fields by expelling them. I don't think there is a particularly compelling argument from the BCS equations, at least not yet.

Sure there is: it drops right out of BCS in fact. An easy way to think of it qualitatively is that the energy for the two electrons in each Cooper pair must be the same or the Cooper pair will dephase, but since the electrons must have opposite spin in order to be in the same spatial quantum state (Fermi exclusion), that means the magnetic field must be zero. Nonzero magnetic fields will "split" the Cooper pairs. You can even predict what the critical field will be (the strength of magnetic field that can no longer be expelled and so will prevent superconductivity) based on the superconducting gap energy.

 

[sol invictus]

Somehow, I located a link to Hyperphysics (someone here must have provided it long ago and I had it bookmarked) where I found that fact in the "superconductors" article, but I am not sure I understand why it is that way.

I don't know if this will help, but one way to understand it is that the photon effectively has a mass inside a SC. That makes electromagnetic forces short range - they die off after a characteristic length (which is the inverse of the mass in natural units), much like the strong force that binds atomic nuclei together. As a result, EM fields can't penetrate very far into a SC, because they damp out rapidly due to the photon's mass.

An even more abstract way to say the same thing is in terms of symmetries. Electromagnetism can be thought of as arising from a certain exact symmetry (rotating the phase of charged fields). In a superconductor that symmetry is broken by the existence of electron Cooper pairs. That breaking of the symmetry gives the photon an effective mass - it means that on distances longer than the inverse mass length scale, electromagnetism is damped out.

 

[Dilb]

Sure there is: it drops right out of BCS in fact. An easy way to think of it qualitatively is that the energy for the two electrons in each Cooper pair must be the same or the Cooper pair will dephase, but since the electrons must have opposite spin in order to be in the same spatial quantum state (Fermi exclusion), that means the magnetic field must be zero. Nonzero magnetic fields will "split" the Cooper pairs. You can even predict what the critical field will be (the strength of magnetic field that can no longer be expelled and so will prevent superconductivity) based on the superconducting gap energy.

That explains why a magnetic field will destroy superconductivity, but that doesn't explain how superconductors spontaneously expel fields. Yes, the superconducting state is lower energy than the regular state, but it's not obvious to me why the transition should be allowed to happen: what exactly accelerates the surface currents when the transition occurs? Is is just a matter of reaching thermal equilibrium, where random thermal noise gets built up into larger currents because each increase improves the cooper pairing?

 

[sol invictus]

That explains why a magnetic field will destroy superconductivity, but that doesn't explain how superconductors spontaneously expel fields. Yes, the superconducting state is lower energy than the regular state, but it's not obvious to me why the transition should be allowed to happen: what exactly accelerates the surface currents when the transition occurs? Is is just a matter of reaching thermal equilibrium, where random thermal noise gets built up into larger currents because each increase improves the cooper pairing?

Zig can correct me if I'm wrong, but I believe the SC transition is always second order - which means that yes, random thermal noise is enough to initiate the transition (which then builds up until it reaches the new equilibrium).

 

[Dave Rogers]

Question: As the field is "dialed" up, I would assume that the current carriers would slowly deviate from purely axial to increasingly helical; would the lengthening of the path taken cause the resistance (voltage vs current) to increase, and could this be used to measure field strength (or is this just some variant of something simple like the Hall Effect)?

Essentially, yes, although it's not quite that simple and there are other effects that may dominate. Magnetoresistance^WP is a well-understood phenomenon and is widely used in magnetic field sensors; a magnetoresistance sensor is easier to engineer than a Hall effect sensor because it only requires two wires and has less dependence on the detailed geometry of the sensor. In high mobility semiconductors the magnetoresistance can be comparable to the zero field resistance; in some rather more exotic two-dimensional systems it can be much larger. In magnetic metal thin films there's a much stronger effect called Giant magnetoresitance^WP, which is widely used in magnetic sensors and hard disk read heads.

Dave

 

[Ziggurat]

That explains why a magnetic field will destroy superconductivity, but that doesn't explain how superconductors spontaneously expel fields. Yes, the superconducting state is lower energy than the regular state, but it's not obvious to me why the transition should be allowed to happen: what exactly accelerates the surface currents when the transition occurs?

As sol mentioned, it's a 2nd-order transition. Thermal fluctuations bounce some electrons into the superconducting state in small regions, and these regions grow in size as you cool the system (or drop the field) until the whole thing superconducts. Furthermore, the number of electrons in the superconducting state increases the farther you get from the transition. Among other things, this also means that the critical field is temperature-dependent, and approaches zero as the temperature approaches Tc from below. If you've almost totally thermally depopulated the superconducting state, then it hardly takes any field to finish the job, because the electrons can't handle a large surface current.