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Homework Help: Magnetic field between two wires (vector sums)

  1. Apr 17, 2010 #1
    1. The problem statement, all variables and given/known data
    Two parallel wires carry a current I and 2I in different directions. What is the magnetic field halfway between the two wires?

    2. Relevant equations
    Ampere's law
    Int (B dot dA) = permissivity x enclosed current

    3. The attempt at a solution
    Draw a circle around wire 1
    B x 2 pi r = mu x I
    B = mu x I / 2 pi r
    if d = distance between two wires, r = d/2

    Where I'm confused is at the part where I add the two B vectors to find the total B. According to the rule of vector addition, I can add vectors to find the net vector. BUT I thought Ampere's law was supposed to describe all of the B at a point as proportional to ONLY the current inside and that currents outside the Amperian loop were not supposed to make any net contribution to B. So how can I add together two vectors when Ampere's law is supposed to describe a magnetic field with all the B vectors already added up? This is a more conceptual question. Thanks.
  2. jcsd
  3. Apr 18, 2010 #2


    User Avatar
    Science Advisor
    Homework Helper

    Hi quantum13! :smile:

    (have a mu: µ and a pi: π and btw, it's permeability for magnetism :wink:)
    You have to look at the whole loop.

    A loop C around a wire with currrent I1 and field B1 has an integral of ∫C B1.dl = 2πrB1 = µ0I1.

    The same loop has an integral of ∫C B2.dl for a different wire, but B2 will not be constant, and if this wire lies outside C, the integral is zero. :wink:
  4. Apr 18, 2010 #3
    hooray another annoying and difficult realization in the land of physics :)

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