# Magnetic lines of force and magnetic flux

## Main Question or Discussion Point

"The number of magnetic lines of force passing through any area in a magnetic is known as magnetic flux" So the definition of flux goes.

But I find it rather ambiguous and loose. Or is that I am missing some vital point?

The magnetic lines of force are not real, they are imaginary lines of force which we draw using a north pole. We can draw as many as we desire using a different starting point for our drawing of lines of force. (Of course, we say that we say that when the strength is more we draw the lines closer and when it is less, we draw them sparse, but it is still subjective, one can start at a different point and draw as many lines as he wants.)SO how can we depend on the number of lines for the definition of flux? Is there no better definition? We can straight forward define it as B.dA perhaps which is less ambiguous.

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rock.freak667
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The number of field lines per unit cross-sectional area is directly proportional to the magnetic flux density.

But my definition of magnetic flux density has to do with a conductor placed at 90 degrees to a magnetic field.

"The magnetic flux density of a magnetic field is defined as the Forced acting per unit current on a conductor of unit length placed at 90 degrees to the magnetic field"

$$B=\frac{F}{Il}$$

Nowadays although we believe in the existence of magnetic fields, magnetic field lines themselves are only a tool for visualization or calculation. It would be better to say the following:
"The magnetic flux determines the number of magnetic field lines passing through any area in a magnetic field"

So we start with a magnetic field, and use the flux to figure out how densely spaced we should draw our field lines.

However, there is a dual description of electromagnetism in terms of flux tubes being fundamental, although I believe the math is quite complicated.

Lbrits, that is my point. we draw crowded/sparse number of lines depending on the strength of the magnetic induction, the basic thing is B, the lines are only pictorial representation, so we better define the flux based on B.A where B is magnetic induction, and A is area with direction of the normal to the surface.

hey lbrits, how are things?

To quote wikipendia,

"To make matters worse, there was a unit of magnetic flux in the obsolete CGS system called the "line" (later called the maxwell) equal to 10-8 webers."

http://en.wikipedia.org/wiki/Line_of_force" [Broken]

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Shooting Star
Homework Helper
Lbrits, that is my point. we draw crowded/sparse number of lines depending on the strength of the magnetic induction, the basic thing is B, the lines are only pictorial representation, so we better define the flux based on B.A where B is magnetic induction, and A is area with direction of the normal to the surface.
The magnetic flux through a surface is defined in exactly the same way as the electric flux:

B.da, where the integral is over the surface.

I don't think the magnetic field is any more real than the magnetic flux. In any case, B may be thought of as a flux density.

Shooting Star
Homework Helper
I don't think the magnetic field is any more real than the magnetic flux. In any case, B may be thought of as a flux density.
Yes, it's all in our minds. Since we have agreed on that, I won't mention it explicitly every time.

Just as a static charge affects another charge through the something called the electrostatic field, so does a moving charge or a current has an additional effect on a moving charge through the magnetic field. How we define it is our choice; to quote from Wikipedia: "for example via the Lorentz force law, or as the solution to Maxwell's equations". We also know that electrostatics and special relativity together can account for a magnetic field. (This also indicates that perhaps magnetic forces and relativity together may, I repeat, may account for the electric forces.)

The fact remains that the flux is defined as the integral mentioned, notwithstanding the earlier historical interpretations of lines of force etc.

Yes, it's all in our minds. Since we have agreed on that, I won't mention it explicitly every time.
I didn't mean it in that sense. These things are very real. I just meant that they are on equal ground mathematically.

To address the statement that B can be explained from E and SR, there are configurations of E and B in which you would need to move into a superluminal frame in order to eliminate B. This depends on the sign of the Lorentz invariant quantity $$E^2 - B^2$$. E is also (roughly) the canonically conjugate momentum to B.

But I think everyone understands everyone else at this point =)

Shooting Star
Homework Helper
But I think everyone understands everyone else at this point =)
Whew, that's relief! So, which quantity you feel should be regarded as more fundamental, even though mathematically we can choose any of them. This is not a trivial question, since lines of thought in theoretical Physics may be, or actually are, guided by such paradigms.