Interpretating magnetic field

  • #1
Hello, I have recently been doing homework about magnetic dipoles, and one doubt has come to my mind; Does a dipole pointing in ine direction produces a negative field in the contrary?.
http://en.wikipedia.org/wiki/Dipole#mediaviewer/File:VFPt_dipole_point.svg
That is what this image seems to sugest.
And the equation http://data:image/jpeg;base64,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 seems to comfirm it for negative r, but for me this seems a little weird.
Can anyone confirm this?
Since the images don't work, the first one is the standard drawing of the dipole's field and the second is the standar formula for B, the first one which appears on wikipedia
 

Answers and Replies

  • #2
386
5
What do you mean by 'negative'? Magnetic field is usually represented as a 3-D vector field. I don't the negativity of a vector field is actually defined since it is a geometrical object. Perhaps, you mean the components in a specific coordinate system. But then you need to define the coordinate system.

And which bit exactly that you feel weird about?
 
  • #3
Actually I am trying to apply Lenz's law to a circular wire and a dipole which is moving on the z axis. The wire is on the plane z=0 and the dipole is at z>0 on the centre of the wire, so it is the z coordinate the component the one which is moving.
And what I feel weir about is that I normaly don't extract the geomretrical meaning of a drawing, but I focus on extracting information from the equations I have at hand, so I don't have much experience with this.
 
  • #4
386
5
I think along the central axis, the magnetic flux density is alone the same direction. It is a common feature in sourceless fields to satisfy Gauss Laws, but to satisfy Ampere's law the off-axis z components have to be negative in some regions.

The drawing of magnetic field is representing the direction of flux density, and I think it is very literal. I do not understand where to confuse about
 
  • #5
Well, I was confused about how the interpretation of the camp lines passing through a region of space and how the movement of the dipole changed them, but I have already understood it. Thanks for your anwser.
 

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