# Magnetic field lines What do they exactly mean?

1. Sep 25, 2010

### mishrashubham

Now this might seem like a really stupid question but I'm just a high school student so please bear with me.

I've been studying about magnetic fields and my teacher says (everyone does in fact) that in a magnetic field, the magnetic field lines start from the north pole and end in the south pole. What does she mean by that? I mean magnetic lines are just a way to represent the magnetic field and flux. So what do we mean by the 'direction' of the magnetic field. What does is signify? For example direction of a force on a body gives us the direction of acceleration which gives us the direction of the velocity. So what does this direction tell us about?

And another thing.... I've read that the electromagnetic force carrier is the photon, and that too a virtual photon. So is this photon the same thing that we associate with light (because those are called real photons) or are they different? Also by terming them as virtual, do we mean that they are abstract concepts and that a name is given to them just for the sake of reference?

2. Sep 28, 2010

### Staff: Mentor

Put a small magnetic dipole such as a compass needle somewhere along a magnetic field line. The "north" end of the dipole points along the direction of the field line.

If magnetic monopoles existed (they don't, so far as we know), a "north" monopole would "feel" a magnetic force in the direction of the field line, just like a positive charge "feels" an electric force in the direction of an electric field line.

3. Sep 28, 2010

### HallsofIvy

The magnetic field lines show the path an object would take if it were attacted to one pole of magnet (and, of course, repelled by the other).

Yes, the "photon" that "carries" the electromagnetc force is exactly the same as the "photon" of light. If you look up at night at a star 1000 light years away, you "see" it because electrons in your retina are reacting to the electromagnetic fields many electrons in that star put out 1000 years ago.

4. Sep 28, 2010

### mishrashubham

Then why do they call light photons real and force carrier photon virtual?

5. Sep 28, 2010

### pallidin

Light photons can easily continue to exist outside of the environment which "created" them.
Virtual photons do not do this.
That is, you can not "emit" a virtual photon to go across a room like one might do with the light from a flashlight or laser.

Most importantly, virtual photons are only real because certain mathematics provide for them. They have NEVER been experimentally proven to actually exist like a "real" photon.
Their existence is inferred.

6. Sep 28, 2010

### nonequilibrium

The direction of a magnetic field is important in for example $$\vec F = q \vec v \times \vec B$$ (this is called the Lorentz Force, or at least the magnetic term of that force), so the direction of your magnetic field determines in what direction a proton in a magnetic field will bend.

As for the physical meaning of magnetic fields, that is a less obvious answer. Feynman talks about this in his lectures and I vaguely remember that it's simply a mathematical formalism that works well and that we shouldn't get hung up on any one way of picturing magnetic fields, implying that we -as humans- can't imagine the "correct" way -a bit like Bohr said we can't really explain quantum mechanics, because we only know everyday concepts in our brains, and those can only vaguely describe the odd quantum world (inherently so, this is not just a lack of vocab)- or implying that we just haven't found the right way yet. I'm not up to date on modern physics and his lectures were from the 60's somewhere, so things might have changed, but not that I've heard of.

Now the very interesting question of virtual vs real photons: I've wondered about the same thing, but I don't know the answer myself (only a 2nd year undergrad). It's interesting that the two answers on that question are contradictory (one saying it's pretty much a normal photon, the other one taking a different more subtle and careful route). For one thing, they can't just be "normal" photons, because then an electron would radiate all its energy in the virtual photons making up his electric field. Good luck on this question, I am curious myself :)

7. Sep 28, 2010

### Staff: Mentor

8. Sep 29, 2010

### mishrashubham

Ok, so the direction of the "field" gives us the direction where the compass would point.

Yes I am aware of F=qvB . But this implies that the direction of magnetic field exists for the sole reason that it is used in formulas like these. But why were they made in the first place? Or is it just for the sake of convention that we still follow it in order to use the formulas that involve it (just like we take direction of current to be positive to negative instead of the actual movement of electrons that is from negative to positive so that we could use it in formulas and things like Fleming's left hand rule)? Because I'm still not able to understand its significance apart from its use in formulas.

9. Sep 29, 2010

Magnetic field lines are imaginary constructs only.They don't actually exist but the concept of field lines can be useful with several problems.In addition to the definitions above a magnetic field line can be defined as the path which would be followed by a small isolated magnetic north pole(imaginary monopole) if it were free to move under the influence of the magnetic force only.From these definitions magnetic field lines go from N to S.Why N to S and why not S to N?There is no good reason except that the definition was made years ago and it has just stuck and been accepted.Why bother to give magnetic field lines a direction in the first place?It does seem daft but by giving magnetic field lines a direction we can work out all sorts of problems such as which way a motor will turn.

Last edited: Sep 29, 2010
10. Sep 30, 2010

### Born2bwire

The whole point is that classical electrodynamics (and of course quantum) is a theory that describes the electromagnetic force. This force results from the interaction between charges. The entire theory is a set of rules to describe this using the concept of force-fields. This is no different from the idea of a gravitational field. Gravity is the mutual attraction between masses (and in Newtonian physics) is a simple static relationship. So we can easily use the gravitational force equation directly (Gmm/r^2) or we can use the concept of a field creating a force on a mass sourced by the other mass.

For gravity this is fairly simple and we do not really think to use an actual field for calculations since we can easily treat the masses as collective sources and add them up discretely. It is much more difficult in electrodynamics to work directly with the charges and their forces because most systems have large numbers of charges and the charges have a different set of forces when they are static and when they are moving. For the static case, it's just like with gravity. We can think of the force directly between the charges (kq_1q_2/r^2) or we can think of it as a force field (F = q_1*E where E = kq_2/r^2). But then it gets tricky with the force that arises due to relative movement and we represent that with the magnetic field.

So the field picture frees us from having to work with large numbers of charges or complex charge distributions and from the bookkeeping of finding the forces both due to their inherent static force and the force due to relative velocities.

11. Oct 2, 2010

### mishrashubham

Ok I just checked this http://en.wikipedia.org/wiki/Field_line.
And it said that a field line line is locus of points defined by a field vector. Understanding vector fields properly involves the use of calculus, with which I am not well versed. But what I know is that a locus is a collection of points that shares some property. So what property do the points on a field line share (magnetic field strength??). I don't know. Or is it again out of the bounds of my knowledge (containing calculus)?

12. Oct 2, 2010

### Born2bwire

You do not need to know calculus to understand vectors or vector fields. A vector is simply a quantity that represents independently a direction and magnitude. A vector field is a mapping of vectors to points in space. A field is simply a mapping of scalars to points in space. We then need to assign a physical interpretation to these fields. In the case of electric and magnetic fields, they are force fields. That is, the fields relate the force that would act upon a test charge at that point in space. The relationship between the field and the force is given by the Lorentz force.

For the electric field, it is very simple as the force and fields are related as
$$\mathbf{F} = q\mathbf{E}$$
So the electric field represents the magnitude and direction of the electrical force that would act on a positive unit charge at a given point in space. The magnetic field is more complicated by the fact that it is dependent upon the velocity of the charge,
$$\mathbf{F} = q\mathbf{v}\times\mathbf{B}$$
So the curl of the charge's velocity with the magnetic field gives us the force for a positive test charge.

13. Oct 2, 2010

### mishrashubham

I couldn't understand what you meant by "mapping of vectors or scalars". Could you please elaborate?

14. Oct 2, 2010

### Born2bwire

A scalar field assigns a scalar value to each point in space. A vector field assigns a vector to each point in space.

15. Oct 2, 2010

### mishrashubham

So does it mean that all points on a field line have the same vector?

16. Oct 2, 2010

### Born2bwire

No. A field line is just a visual representation of a vector field. However the rules are not set in stone and it is meant to be a visual approximation. Generally, the lines, along with associated arrows, will indicate the direction of the vector field. The magnitude is generally not directly shown but generally the density of the field lines gives a relative indication of the strength of the fields.

17. Oct 3, 2010

### mishrashubham

Ok so what I gathered from all the answers above is that the direction of magnetic field lines does not define the direction of some precise physical quantity but is just there by convention and that its sole purpose is to be used in formulas and to find the directions of other things like force, current or velocity of moving charge.
Am I right?

And as for virtual photons it seems that they are simply "mathematical constructs" developed for the purpose of fitting in some mathematical equations. Though I am still unclear about real and virtual photons. Because a few years back it took some time to take in the fact that what we call contact forces are actually non contact electromagnetic forces acting on the microscopic scale. But this seems to be bringing the non contact forces back to aspects of contact forces by thinking virtual photons are emitted by two electrons and as a result of this exchange they recoil back which is visible as an effect of force.

18. Oct 6, 2010

### Born2bwire

As to the first statement, yeah though I would just say that they are not a direct indicator of a physical quantity but indirectly by virtue of the fact that you still need to know the velocity of your test charge to find the magnetic force. Though in practice we do not really use such intermediate steps for a lot of things, like finding the force between two current carrying wires we can work directly with currents and magnetic fields via Maxwell's equations. The Lorentz force is the underlying relationship between the fields and the physical forces that they describe but we can get a vast array of information by working with the field equations given by Maxwell without explicitly introducing the Lorentz force.

Yeah, virtual photons are mathematical constructs and in a way they aren't. A virtual photon is a photon that pops in and out of the vacuum on a very short time scale. What happens is that, as described by the Heisenberg Uncertainty Principle, if we observe a system over a very very short time scale, then we will see a large variance in the observed energies of this system if we repeat the experiment identically over a large number of times. Now over a long time scale we should see the observed energies only have a small variance (range of values about the mean).

So what happens is that over a short time scale, a large energy fluctuation can momentarily occur. This can have enough energy to create a photon. This photon carries the energy of the fluctuation and then it returns to the vacuum and gives up the energy. So the energy fluctuation can be thought of as a momentary creation then annihilation of a photon. This is done on such short time scales that it is not observable and thus we consider the photon to be "virtual." But there are real world consequences of this virtual photon as it gives rise to the static forces (and more recently it popped up again in the context of Hawking radiation). And since these virtual photons do not persist and quickly return to the vacuum, in the long run over we observe consistent energy observations.

But since this virtual photon is not observable, we can't say that it is truly real. So for now it is best to consider it a mathematical construct but its consequences are observable.

19. Oct 6, 2010

### nonequilibrium

Well you'd still have to use the direction of the current, just like the direction of the electron in the other case. And although the Maxwell's equations give a lot of info, they give nothing physical until one also uses the Lorentz force equation, right?

20. Oct 6, 2010

### Born2bwire

No, though I would agree that it is working in the background of all things. The easiest thing to do would be to find the energy of the system and take the gradient to get the force. This can be seen with any intermolecular force derivation involving dipole moments and such. I don't contend that this avoids the Lorentz force, it's still plugging away in the background, but a lot of times we can use the field and source relationships of Maxwell's equations and get forces and dynamic results (like how a magnetic field induces a current in a wire loop) without directly invoking the Lorentz force equation. Another example would be electromagnetic simulations to find the received power or current from an antenna due to an excitation field. We can just use Maxwell's equations without use of the Lorentz force and get the currents and power transferred and so forth.

21. Oct 6, 2010

### mishrashubham

Thanks, that cleared a lot of things.
So light photons (the ones which are real) are the same as virtual photons but they are called so because of the extremely small and unobservable time period in which they exist. Therefore, they are not experimentally proven but their effects can be seen as forces.

Thanks again.

22. Oct 6, 2010

### mishrashubham

I've got one more doubt. I just read this http://en.wikipedia.org/wiki/Electromagnetic_radiation. And it says "Electromagnetic radiation (often abbreviated E-M radiation or EMR) is a phenomenon that takes the form of self-propagating waves in a vacuum or in matter. It comprises electric and magnetic field components, which oscillate in phase perpendicular to each other and perpendicular to the direction of energy propagation."

What does it exactly mean by electric and magnetic components? And if magnetic field is not supposed to represent any physical quantity then what is meaning of
"According to Maxwell's equations, a spatially-varying electric field generates a time-varying magnetic field and vice versa. Therefore, as an oscillating electric field generates an oscillating magnetic field, the magnetic field in turn generates an oscillating electric field, and so on. These oscillating fields together form an electromagnetic wave."

So EMR is made of oscillating fields. But isn't a field something that is used to show the region of influence of a magnet or charge? It is not a physical quantity. Then how is it supposed to oscillate. Or does oscillate mean something other than moving to and fro periodically, in this context?

23. Oct 6, 2010

### Born2bwire

An electromagnetic wave is produced by the acceleration of charges. This can be an oscillating charge (AC current) but it could also be a charge that is being linearly accelerated or moving in a circular motion (synchrotron radiation). But conceptually it is easiest to visualize it as an oscillating charge or set of charges.

An electromagnetic wave always consists of an electric field and a magnetic field which are oriented normal to each other. As such, we always talk about the electric and/or magnetic component of the wave. The two fields are related to each other by a constant and phase offset and thus it is generally sufficient to only talk about one of the fields since we can easily infer the behavior of the other field.

If you wish to think purely in terms of the source -> field -> force, then perhaps you should look at Jefimenko's Equations. Jefimenko's Equations are a set of equations for the electric and magnetic fields derived by solving the complete Maxwell's Equations. The field equations are dependent only upon the source currents and charges and thus this presents a more causal picture of the fields due to their associated sources.

Thus, if you substitute Jefimenko's Equations into the Lorentz Force Equation, you can get a complete force relationship that is only explicitly dependent upon your sources. But as you can quickly see this is a very cumbersome method to use. In addition, it always requires the explicit inclusion of sources where as in the field view we can explicitly choose a desired field excitation without worrying how we create this field via sources. As long as the excitation follows Maxwell's Equations it should theoretically be produceable.

http://en.wikipedia.org/wiki/Jefimenko's_equations