1. Not finding help here? Sign up for a free 30min 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!

Determine the magnitude of the magnetic field.

  1. Oct 4, 2013 #1
    1. The problem statement, all variables and given/known data

    Three long parallel wires are 3.5 cm from one another. (Looking along them, they are at three corners of an equilateral triangle.) The current in each wire is 8.00 A, but its direction in wire M is opposite to that in wires N and P. Determine the magnitude of the magnetic field midway between points M and N.

    2. Relevant equations

    ##B = \dfrac{\mu_0 I}{2\pi r}##

    3. The attempt at a solution

    First, I compute the field due points M and N, which is

    ##B_{MN} = \dfrac{2\mu_0 I}{\pi d}##

    Then, the field due point P is

    ##B_P = \dfrac{mu_0 I}{\pi d\sqrt{3}}##

    Working component wise, I obtain:

    ##B_x = B_{MN}\cos(30) + B_P\cos(60) = \dfrac{7}{2\sqrt{3}}\dfrac{\mu_0 I}{\pi d}##
    ##B_y = -B_{MN}\sin(30) + B_P\sin(60) = -\dfrac{\mu_0 I}{2\pi d}##

    So we have

    ##B = \sqrt{(B_x)^2 + (B_y)^2} \approx 9.52 \times 10^{-5}##

    But the answer is wrong.
     

    Attached Files:

    Last edited: Oct 4, 2013
  2. jcsd
  3. Oct 4, 2013 #2

    TSny

    User Avatar
    Homework Helper
    Gold Member

    Hello, NasuSama.

    Check to see if you got the correct distance for ##r## for wire ##P##. [Nevermind, I think you got it right!]

    It looks to me that some of your trig functions are incorrect in finding the x and y components.

    You might consider rotating the whole system so that M and N are at the base of the triangle.
     
  4. Oct 4, 2013 #3
    I am not sure if rotating the system works.

    Other than that, I edit my trig functions since I found they are incorrect by typos.
     
  5. Oct 4, 2013 #4

    TSny

    User Avatar
    Homework Helper
    Gold Member

    If you don't want to reorient the system, then let your x-axis pass through wires M and N and the y-axis pass through P and the midpoint of the line segment MN.
     
  6. Oct 5, 2013 #5
     

    Attached Files:

    Last edited: Oct 5, 2013
  7. Oct 5, 2013 #6

    TSny

    User Avatar
    Homework Helper
    Gold Member

    Looks good!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted