1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Magnetic field of infinite wire

  1. Feb 4, 2015 #1
    1. The problem statement, all variables and given/known data
    An infinite wire carries current I.


    I hope the picture works! The vertical arrow shows the direction of current in the wire. The green arrow has length a and ends at point P. What is the magnitude of the magnetic field at point P?
    2. Relevant equations
    dB = (μ/4π) (I dl×r )/r3
    Where the r on the numerator is a position vector.

    3. The attempt at a solution
    The horizontal part of the wire is irrelevant, as l is in the same direction as r at that point.

    r is the distance of P from the vertical wire, I think. I called the direction of the green arrow the positive x direction, the direction of current and of dl is the y direction. I have to find the magnitude of the field, so I have to integrate the expression for dB. dl can be replaced with dy as they are in the same direction.

    I, μ and 4π are constants and can be taken out of an integral. The magnitude of the cross product on the numerator is given by r dy sinφ, where r now cancels with the r in the denominator.
    I have to do (μI / 4π) ∫ (dy sinφ) / r2
    So the distance r to the wire will be given by Pythagoras' theorem, so r = (x2+y2)1/2.
    My major problem is, I don't really know which angle φ is. It's one of two! Is sinφ given by x/(x2+y2) or should y be on the numerator instead?

    Anyway, I carried on assuming x is on the numerator. Then the integral becomes:
    ∫ x dy / (x2+y2)3/2

    So do a substitution of y=xtanφ. And then how I carry on really depends on what angle φ is!
    Thanks for any help :)
    Last edited: Feb 4, 2015
  2. jcsd
  3. Feb 4, 2015 #2
    Oh, and all black lines indicate a part of the wire, which does turn a corner.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted