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Homework Help: Magnetic Field of rectangular current loop

  1. Mar 1, 2010 #1
    1. The problem statement, all variables and given/known data

    Find the magnetic field of a rectangular current loop lying symmetrically on the xy-plane. Find the magnetic field at (0,0,z)

    2. Relevant equations

    Biot-Savart law or derived formula (Mu/4*Pi) * sin(theta2)-sin(theta1)/s

    3. The attempt at a solution
    I am NOT good with getting my trianges correctly. I know that B1=B3 and B2=B4 but I cannot figure out the values of the thetas!
  2. jcsd
  3. Mar 1, 2010 #2
    Try and show a little more work than what you've got.
  4. Mar 1, 2010 #3
    Well I know how to solve it for a square loop theta 1 =-theta2=45 degrees
    = sqrt2*Mu*I/Pi*R
    Now for a rectangle I think that theta1=-theta2 (for sides B1=B3) = -b/(sqrt(a^2+z^2)
    and theta1=theta2 (for sides B2=B4) = a/(sqrt(b^2+z^2) and than I add them together but I'm not sure
  5. Mar 2, 2010 #4
    Noone can help me with this question?
  6. Mar 2, 2010 #5
    This is actually pretty tough. You're going to have to use the Biot-Savart law from scratch. The formula you're trying to use is for a point in the same plane as the wire, and isn't going to work here.

    [tex]\mathbf{B}(\mathbf{r})=\frac{\mu_0 I}{4 \pi} \int \frac{d \mathbf{l}\times \hat{\mathbf{r}}}{r^2}[/tex]

    You should realize some amount of symmetry. I remember I worked this out once, because I was making rectangular coils for a magneto-optical trap, and it took me a bit. What level of physics is this?
    Last edited: Mar 2, 2010
  7. Mar 2, 2010 #6


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    Gold Member

    Slight modification: notice that it should read [tex]\mathbf{B}(\mathbf{r})=\frac{\mu_0 I}{4 \pi} \int \frac{d \mathbf{l}\times \mathbf{r}}{r^3}[/tex].
  8. Mar 2, 2010 #7
    Oops, yeah, I forgot the hat, I'll fix mine and let yours be an alternate. :)

    Edit: Nvm, the hat on the r vector isn't working... so the later version is the best.
  9. Mar 2, 2010 #8
    It's third year...E&M 2..any help? I do know there is symmetry of the horizontal and vertical components, and they all add up to give the total magnetic field
  10. Mar 4, 2010 #9
    Actually, I've been thinking about this. You can use the derived result that you mentioned earlier, or start from scratch from Biot-Savart. Either way, it's your homework and not mine. You have to make the effort. If you have, then show use you've made the effort by posting some work.
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