# Magnetic Field

Discussion in 'Homework Help' started by Debdut, May 4, 2012.

1. ### Debdut Thread Starter New Member

Aug 26, 2011
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What is direction of magnetic field?Are there any difference between magnetic field or magnetic field lines?Why magnetic field lines do not intersect?

2. ### MrChips Moderator

Oct 2, 2009
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Magnetic field lines do not exist. It is a pictorial or graphical aid to illustrate the direction of the magnetic field at any given point.

An analogy would be contour lines on a topographical map. In real life, contour lines do not exist. You do not see lines of equal elevation drawn around mountain peaks.

Also, you will never see contour lines crossing.

3. ### amilton542 Active Member

Nov 13, 2010
494
64
@ MrChips

I find it hard to believe magnetic field lines don't exist. If you sprinkle iron filings around a bar magnet or, on the converse, place grass seeds inside an electric field, then one will see the direction of flux by way of the lines.

4. ### WBahn Moderator

Mar 31, 2012
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Here's the more difficult thing to get your mind around - magnetic fields don't exist, either. Like centrifugal force, magnetic fields are a mathematical construct that explain certain phenomenon from within a reference frame that makes the application of the fundamental forces difficult. If you jump into the reference frame of the moving charge that we say is being affected by a magnetic field and apply the Lorentz transformations to the charge distributions that are responsible for what we call the magnetic field, you end up with an electric charge distribution that exerts the same force on the charge as the we say the magnetic field does.

As for why magnetic field lines don't cross, the analogy with contour lines is useful, but not really applicable. Contour lines are isometric lines, meaning that some metric is the same anywhere on the line. In the case of a topographic map, the metric is elevation. Adjacent contour lines are at different elevations, so if they ever crossed, it would require that the same point on the ground was at two different elevations. Now, some maps do have to deal with this situation. There are places where there are overhangs sufficiently large such that the topology of the ground both on top of the overhang and underneath it would be discrenable on a map and, in some contexts, such as orienteering, the information about both can be relevant. Usually, you can just plot both sets and let the reader discern which is which since the lines are continuous leaving the overlapping area.

Getting back to magnetic field lines, they aren't usually described as being isometric lines, so this argument doesn't apply directly. Instead, they form closed circuits and a charged particle travelling along the circuit would feel no force due to the field. It is probably reasonable to interpret this as a description of lines of constant magnetic potential, in which case they do have to behave the constraints on isometric lines, including no crossing. But even if they don't, it would mean that if lines crossed, you would have points where a charge could move in one of two directions from the same point, which creates problems.

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5. ### MrChips Moderator

Oct 2, 2009
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Yes, I realized contour lines are isometric lines but I couldn't think of another analogy.

Magnetic lines show direction a monopole would travel. If you had lines that are crossed then there would be two different directions and a monopole would be confused, which is a problem as WBahn says.

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6. ### crutschow Expert

Mar 14, 2008
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3,362
The direction of a magnetic field from a coil carrying a current is determined by the right-hand rule. Point the fingers of the right hand in the direction of the current through the coil and the thumb points in the direction of the field (north pole to south pole) from out the center of the coil. (You use the left-hand rule if you talk about electron flow direction rather than current).

7. ### amilton542 Active Member

Nov 13, 2010
494
64
This is what I don't get, if the claim is made that a magnetic field doesn't exist, then what is it?

In a similar way, how can you be given a direction without a line to follow?

If all the external claims are true, then elementary physics is poison.

8. ### MrChips Moderator

Oct 2, 2009
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3,451
Imagine that you held a compass in your hand and you walked in the direction that the compass needle is pointing. There is certainly a defined direction but there is no line drawn on the ground nor a rope that pulls you along. The magnetic line of force is an imaginary concept.

9. ### WBahn Moderator

Mar 31, 2012
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Imagine you and a friend are sitting on a real smooth running merry-go-round on opposite sides of the rim while it is turned by a motor at constant speed. Now imagine that it lit in such a way that all you can see is what's on the merry-go-round. It this "world" was all that you ever knew, you would describe everything by mathematical equations that describe what you observe in your world which, to you, is nice an stationary. Thus you would have to come up with a law about your universe that says that the further you get away from the center of the universe, the greater the force is that is trying to pull you directly away from it; you might call this force "centrifugal force". But that isn't the only force you would experience. If your friend on the opposite side of the world throws a baseball straight at you, it wouldn't come at you even though the centrifugal forces are acting radially. Instead, the ball would be deflected sideways. After much study and data collection, you would discover the mathematical equations that correctly describe this motion and you might call the force responsible the "Coriolis force". You also have a pretty complicated set of equations, that you call Newton's Laws, that relate how objects move when they are acted on by contact forces and those equations depend on what direction the force is acting in.

Now, it is merely mathematical gymnastics to translate these equations of motion into other reference frames and eventually someone gets curious and works out a reference frame that suddenly makes both the centrifugal and the Coriolis forces go away and now all motion is described by just a very simply version of Newton's Law that acts the same in all directions. Some people then assert that this is a preferred reference frame that should always be used and that the other forces don't exist. Others point out that all forces are reflective of the reference frame in which they apply and no force is any more 'real' than any other force; they all simply describe how things interact within a given reference frame and if a 'force' validly describes those interactions in the world in which we live, then it is a valid force.

Who is right? Is either view right? That's a question that gets into a lot of philosophical mud. Still, even those that most ardently argue for the 'existence' of the centrifugal and Coriolis forces will acknowledge that the existence of a reference frame in which those forces cease to exist is interesting, profound, and enlightening.

So it is with magnetic fields. They are a useful and valid mathematical construct in the reference frame in which we operate, but none-the-less it is interesting, profound, and enlightening that reference frames exist in which they don't.