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I The difference between Ampere's law & Biot-Savart Law

  1. Jan 3, 2017 #1
    When considering the magnitude of the magnetic field at a certain point (##P##) away from an infinite/finite wire, I can't understand how an infinite wire would generate a stronger magnetic field (##B##) in contrast to a finite wire that has the same dimensions and current applied, at the same point (##P##). I understand how to use the equations, yet I can't fully understand the concept.

    Considering the case of an infinite wire:
    Case1.jpg
    At the point the magnetic field is point out of the page.
    Case of the finite wire:
    Case2ab.jpg

    Where (A) is the current element region of focus.
    Why are the different considering the same ##I## and dimensions for the two?
    I found from other sources that all the current elements in the wire would contribute to the magnitude at point(##P##) but how is that so? If the magnetic field created by the current element loops around it:
    Side_View.jpg
    If so, how can regions B,C contribute to point(##P##) for the two wires?
    Case2.jpg
    For the finite wire:

    Case2b.jpg
     
  2. jcsd
  3. Jan 3, 2017 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    That is not the full magnetic field induced by the wire element. The full magnetic field is 3-dimensional, it just has its strongest region orthogonal to the wire.

    You can use Biot-Savart to calculate that.
     
  4. Jan 3, 2017 #3
    For some reason I can't imagine that...
     
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