Questions related to magnetism

[eightsquare]

I'm studying magnetism from my textbook, and I have several doubts.
1. Magnetic flux in my textbook is defined as the number of magnetic field lines passing through a surface held perpendicular to the lines. However, the unit given is Weber- N.m/A
How do 'no. of magnetic field lines' connect to a unit that has no apparent relation to 'lines'?
2. The textbook says that magnetic poles are formed due to an imbalance of north poles at one end and south poles at the other end. There is no other electron to neutralize them. Then why are magnetic poles not at the extreme ends of the magnet? The reason given is 'The positions of the poles are conjectured to be the points inside the magnet where the field lines appear to meet when extrapolated'. What does this mean?
3. I think the magnetic moment of a bar magnet is constant. Is this right?
4. According to what I read an electrons electrostatically repel each other but can magnetically attract each other. However I know that electromagnetism is a joint fundamental force. How do two same particles both attract AND repel each other with the same force?
5. And lastly, I've seen many formulae for induction along the axis of a bar magnet, solenoid, etc. Are these purely experimental or are the derivations of higher level(I'm reading the 11th grade book) and are proved later on?

Thanks a lot.

 

[technician]

In the early days of magnetism (Faraday) the region around a magnet was represented by a 'force field' represented by 'lines of force'.
The strength of the field was represented by the number of lines passing through a square metre...lines /m²... To recognise the contribution to magnetism by Weber the 'line' were called 'Webers'...hence strength = Webers/m²...W/m²

When it was realized that magnetic fields had a very close link to the force experienced by moving charges another relationship emerged:
the force on a charged particle in a magnetic field is proportional to the charge and proportional to the velocity
ie F is proportional to q x v...so F = Bqv...B is the constant of proportionality and is known as the strength of the magnetic field or Magnetic Flux Density and the unit is the Tesla (T).
To tie in with the earlier ideas 1T is taken to represent 1W/m²
You can see that B must also have units that are N/(Cxms^-1)
or units of B are N/(A.m)

So you have a (confusing?) choice 1T = 1Wm^-2 = 1NA^-1m^-1

 

[eightsquare]

You didn't answer any of my questions fully. How are 'magnetic lines' connected to a unit? That's the only question you attempted to answer.

 

[technician]

Sorry...that is all I feel competent to answer.
You need to rely on someone else.

 

[marcusl]

1. Technician is correct in pointing out that modeling fields as lines is a historical artifact that has persisted because we find it helpful to to think of abstract concepts in terms of pictures. The unit is not related to the picture in any fundamental way.

2. Saying that there's no electron to neutralize a pole doesn't make sense as written, and mixes up several concepts. Ferromagnetism arises from strong interactions of electron spins in the material's atoms. This is a quantum mechanical effect that cannot be described classically, and is considerably beyond the level that you are reading right now. Perhaps this is somehow being mixed up into your statement.

Conceptual pole faces are set back a bit from the ends of a bar magnet as an approximation to produce the observed field patterns. Unless the permeability μ were to be infinite (which is not possible), there will be "fringing" of the fields near the ends. That is, not all field lines exit the bar's ends, but some exit "early". This can be approximated by putting the fictitious pole sources back from the ends.

3. I'm not sure what you mean by this. A moment is an average property of an object when looked at from outside of a sphere that surrounds the object. If you mean that it's value is not time varying, then yes, that is correct.

4. To understand this, you need to understand both classical electromagnetics and special relativity. Maxwell's equations are relativistically correct, meaning that they correctly represent the behavior of fields and potentials of sources in motion. It can be shown that what we call the magnetic force is actually the familiar Coulomb electrostatic force as seen in a moving frame of reference. This is why magnetic fields are associated with moving charges (currents). Once you get farther in your studies, you can find discussions of this in the following two college textbooks:
Purcell, Electricity and Magnetism
Griffiths, Electrodynamics

5. Well, all of E&M theory was originally inspired by experimental observations, and was developed to match measured results. The theory is now impressively complete, however, and once you learn it you can apply its equations to predict magnetization and induction. (Have I answered your question?)

 

[eightsquare]

@technician- That's okay. Thanks for trying :)
@marcusl- 1. I did some research and found out that induction quantitatively is equal to a constant multiplied by the pole strength divided by the distance squared. So I understand now that 'lines' are just a historical concept. Pole strength is equal to Magnetic Moment divided by the magnetic length, so I'm assuming that Magnetic Moment of common bar magnets, etc. are due to internal effects are determined only by experimentation?
2. So classically, the concept of magnetic poles not being at the geometric ends is purely due to experimental observation and does not take into effect quantum effects(right?)
3. You answered my question.
4. Okay. However I'm still curious, so if possible, could you give a toned down explanation of the 'moving frame of reference' part? If two electrons electrostatically repel each other how can they attract each other in a moving frame?
5. Yes. So basically like all the other fundamental forces we don't know 'why' but we have matched out equations to predict 'how' and these equations have survived several experimental tests.

 

[marcusl]

@technician- That's okay. Thanks for trying :)
@marcusl- 1. I did some research and found out that induction quantitatively is equal to a constant multiplied by the pole strength divided by the distance squared. So I understand now that 'lines' are just a historical concept. Pole strength is equal to Magnetic Moment divided by the magnetic length, so I'm assuming that Magnetic Moment of common bar magnets, etc. are due to internal effects are determined only by experimentation?

I'm not familiar with describing a bar magnet by a single moment, so I won't comment.

2. So classically, the concept of magnetic poles not being at the geometric ends is purely due to experimental observation

Wll, not entirely. You can also predict the fields from Maxwell's equations, using magnetic poles as effective sources. These calculations are not simple, however. You can get a glimpse of the complexity by searching on "demagnetizing fields" and reading the Wiki article and one or two of the university lecture notes on the topic.

and does not take into effect quantum effects(right?)

True, no quantum effects in the classical realm.

3. You answered my question.
4. Okay. However I'm still curious, so if possible, could you give a toned down explanation of the 'moving frame of reference' part? If two electrons electrostatically repel each other how can they attract each other in a moving frame?

See http://en.wikipedia.org/wiki/Relativistic_electromagnetism
for an introduction.

5. Yes. So basically like all the other fundamental forces we don't know 'why' but we have matched out equations to predict 'how' and these equations have survived several experimental tests.

Right. Although in this case we later found a deeper understanding of "why" from quantum mechanics.

 

[eightsquare]

Thank you. I'll see if I have any more doubts. I've almost come to the end of the lesson.

 

[eightsquare]

Okay I think I got a couple more questions.
1. If two charges are moving close to each other, assuming no external influences, the significant value to compute in order to study their motion would be magnetic force, right? This can be computed using the formula magnetic pole strength multiplied by the magnetic induction. I'm assuming electrostatic force would be insignificant here. If the charges are stationary however, the significant value would be electrostatic force found by a constant multiplied by the product of the two charges divided by the square of the distance between them. My point is, since magnetism and electrostatic force are two sides of the same coin, both of them cannot be significant simultaneously, right?

2. I'm not entirely sure if this question belongs here. When we apply a force to an object(contact force), how is it transmitted equally to all particles? For example if I kick a ball, obviously I don't come in contact with the whole ball but the ball moves nevertheless. I'm including it here because it involves electromagnetic force.

Thanks! I find magnetism to be really interesting...

 

[marcusl]

1. Wrong, both are important although for two charged particles the electric force is generally stronger than magnetic. Look up Lorentz force to calculate them both.
2. Objects are solid because of chemical bonds between the atoms.These hold the atoms together into a rigid structure.

 

[eightsquare]

1. If magnetism is just electric force in a moving frame of reference then how can both the forces exist at the same time? Suppose two electrons are stationary. There is electrostatic force between them. If they are in motion there is magnetic force between them. How does electrostatic force also exist at the same time. Doesn't electrostatic force become magnetic force when the frame of reference is moving?
2. So I'm assuming that the uniform distribution of force is due to having to maintain the lowest possible potential energy in the bond?

 

[eightsquare]

Ok I read Relativistic Electromagnetism and I've understood the part about magnetism being due to a moving frame of reference. I would like to present my current understanding about things electromagnetic, and would like confirmations/additional information or telling me where I'm wrong. Currently, I have studied three electromagnetic interactions. The easiest seems to be electrostatic force. It is simply due to the intrinsic property of charge of particles. If the particles in question are at rest, we have a simple formula to determine the force between them.
Secondly, the magnetic field due to an electric current. Although the current carrying conductor is electrostatically neutral due to Lorentz transformations the wire acquires a positive or negative charge in that frame of reference and thus a test charge placed near it experiences a force.
Lastly what seems like 'static' magnetism. I mean magnetism in bar magnets, etc. Of course on the atomic level it is not static. This magnetism is due to the intrinsic property of spin of electrons. I am the most unclear here. Obviously in a bar magnet there is no actual flow of current, so I'm assuming the magnetic field produced has something to do with the spin of the electrons. Does this mean that this kind of magnetism does not affect protons?( It seems unlikely that two electrons with opposite spin will attract a proton differently. Could someone clarify this last bit?

 

[marcusl]

Yes, your first two descriptions here are good. Regarding ferromagnetism, it arises from strong cooperative interactions between unpaired electrons (this goes back to chemical bonds and electron shells/orbitals) in certain materials including iron. The protons are shielded by the electron clouds and cannot participate in this kind of long range coupling, even in crystals.

 

[eightsquare]

Ok, I think I got an explanation for the third case also. An electron has a charge and also has quantum spin. As a charge in motion has a magnetic field associated with it, so does an electron. The normal uniform electrostatic field is transformed into a non-uniform magnetic field due to rotation and the electromagnetic force exerted on another charge depends upon its position relative to the spinning electron. As electrons are paired with opposite spin this magnetic effect cancels out and we don't see random things getting attracted to each other. However if there is lining up of the electrons then there is a net magnetic force and there can be attraction or repulsion. (I'm not clear on the reason here though. In a scenario of a bar magnet attracting a piece of iron, its the electrons that attract right? And is this due to the magnetic field or like the electric current example due to a net electrostatic charge?

And as electrons always have a magnetic field associated with them I'm assuming first we compute the electrostatic field and then appropriately transform it into a magnetic field depending upon the electron's motion?

 

[marcusl]

The picture of an electron spinning and therefore in motion is just that--another picture that we find comforting but that is not really accurate. The electron has a magnetic moment (here is where the concept of moment is useful) that directly produces a magnetic field. It is not appropriate to try to think of the electron moment in terms of an electrostatic field. (BTW, the E field from a charged particle is not uniform in any case.)

You are correct that ferromagnetism is created by long range cooperative interactions between unpaired electrons in the iron's (or other material) atoms.

Even in the classical case, it is awkward to try to calculate magnetic fields by boosting electric fields into a moving frame. This is done, generally, only in particle physics where charges are accelerated to relativistic speeds in colliders. Otherwise, Maxwell's equations are relativistically correct and give magnetic fields from currents and from magnetization directly in one step.

 

[eightsquare]

Thanks. All but one of my doubts have been cleared. Do electrostatic and magnetic forces exist at the same time?(How)?) This would explain how magnets attract magnetic materials, and also how even though electrons repel electrostatically they have opposite spins in the same orbital. It also explains why normal everyday objects don't attract each other as the number of electrons with positive spin is approximately equal to the number of electrons with opposite spin.

 

[marcusl]

Yes, they exist at the same time because they are the same force (electric) as viewed or manifested depending on the frame of reference. You can see purely electric, magnetic or a combination of forces, depending on the scenario.

Your "explanation" of orbitals and ferromagnetism does not follow from that, however--you need quantum mechanics to accomplish that. Electrons are held in place within atoms by electric attraction to the nucleus, more or less. The more or less depends on the atom's electronegativity, which determines the atom's affinity for outer shell electrons. Halogens are desperate to fill their outer shell, so will grab an electron from other atoms. Hence the extreme reactivity of chlorine, as an example. Alkali metals such a sodium, on the other hand, have a nearly empty outer shell occupied by a single electron. They are happy to give that electron up to achieve a configuration of filled shells. In water, table salt NaCl readily dissociates into positive sodium ions and negative chlorine ions. Each electron energy level in an atom can accommodate two electrons with opposite spins, satisfying the Pauli exclusion principle which states that no two fermions can occupy the same state. By having differing spins, these two electrons have different states.

The exclusion principle and the atomic shell model explain the layout of the periodic table. Magnetism follows from consideration of the number and configuration of electrons in the shells, and from more advanced effects such as the exchange interaction which leads to long range order.

The following Wikipedia articles may be helpful:
Electronegativity
Pauli exclusion principle
Atomic orbital
Ferromagnetism

The topics you are interested in are covered in freshman-sophomore college courses. Full explanations with appropriate math typically (in the US) arrive at the junior and senior level with electromagnetism and quantum mechanics. You'll need to be a bit patient to build up the mathematical and physics background to understand them in full detail.

 

[eightsquare]

Ok so for now I can conclude that electrostatic force and magnetic effect due to current are due to classical effects but ferro magnetism is due to quantum effects? And the last question- Even though nucleons and electrons have a permanent magnetic moment, this becomes significant only when there is relative motion- otherwise electrostatic law holds?

 

[marcusl]

Ok so for now I can conclude that electrostatic force and magnetic effect due to current are due to classical effects but ferro magnetism is due to quantum effects?

Yes.

And the last question- Even though nucleons and electrons have a permanent magnetic moment, this becomes significant only when there is relative motion- otherwise electrostatic law holds?

No, electrons and those nuclei that have a magnetic moment have it even at rest. Classically their field is that of an infinitesimal bar magnet--one so small that it is well approximated by a magnetic dipole. As an example, the classical magnetization M of a material is given by integrating the atomic magnetic moments.

 

[eightsquare]

I know that these particles have a permanent dipole moment. Maybe this example could clear things for me even more. Suppose we have to calculate the electromagnetic interaction between an electron and a proton, both at rest. Using the electrostatic law we can find the electrostatic force. Do we also need to find the magnetic force(because even a stationary particle has a dipole moment) and add it to the electrostatic force to get the net force?

 

[marcusl]

Technically, yes. However if you do the calculation (use formulas for the Coulomb attraction, and for the force between two dipoles) you will find that the magnetic force is negligibly small compared to the electric force. Both have been measured in the hydrogen atom. You can check your answer against known results: The hydrogen ionization energy (energy required to overcome the Coulomb attraction and remove the electron) is 13.6 electron volts (eV). The energy difference required to change the e and p spins from an aligned to anti-aligned configuration is 6e-6 eV, so the energy of the magnetic interaction is 3e-6 eV. This is known as the hyperfine structure of the hydrogen atomic spectrum. The magnetic interaction energy is small, only about 0.2 ppm of the electric.

Here is a brief discussion:
http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/h21.html

 

[eightsquare]

Thank you very much for answering all my questions. I'll sum up my understanding, and if its fine, we can close the thread.
The Coulomb electrostatic force of attraction is due to the intrinsic property of charge. The electrostatic force can be calculated using the inverse square law(k*q1q1/r^2). When charges are in motion, this electrostatic field in a moving frame of reference becomes the magnetic force. In a stationary frame of reference this force is still electrostatic in nature. And lastly, due to another intrinsic property, that of quantum spin, particles have a permanent dipole moment, and so have a magnetic field associated with them. However the force exerted by this field is really tiny compared to the electrostatic force and so can be neglected generally. In normal substances, all the small atomic moments cancel out. However in magnetic substances, millions of these tiny moments line up to give a significant dipole moment and magnetic force.

How's that?

 

[marcusl]

Your understanding at this point is good. There is one qualification to add to this sentence:

However the force exerted by this field is really tiny compared to the electrostatic force and so can be neglected generally.

While this is true when considering both electric and magnetic field of charged particles, magnetic material are charge-neutral so no external electric force exists. In this case, the magnetic field is non-negligible (it's all there is) and can be used for practical applications.

Good job!