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!

Magnetic Field at the Center of a Wire Loop

  1. Mar 7, 2008 #1
    1. The problem statement, all variables and given/known data

    A piece of wire is bent to form a circle with radius r. It has a steady current I flowing through it in a counterclockwise direction as seen from the top (looking in the negative z direction).

    What is B_z(0), the z component of B at the center (i.e., x = y = z = 0) of the loop?

    Express your answer in terms of I, r, and constants like mu_0 and pi.

    2. Relevant equations



    3. The attempt at a solution

    I know this equation:

    [tex]\frac{(\mu_0)I}{2(\pi)r}[/tex]

    but there is a hint that says I need to find the Integrand.

    Thank You.
     
  2. jcsd
  3. Mar 7, 2008 #2
    Integrate the magnetic field around the circular path of radius r.
    [tex]\oint \vec B \cdot d\vec r = ?[/tex]
     
  4. Mar 7, 2008 #3

    Doc Al

    User Avatar

    Staff: Mentor

    Biot-Savart law

    That's the magnetic field from an infinite straight current-carrying wire.

    Look up the Biot-Savart law. That will give you the field from a current element.

    Right. Once you have the field from a current element, you'll need to integrate around the entire loop. (Since you are only asked to find the field at the center of the loop--as opposed to some arbitrary location--the integral will turn out to be quite doable.)
     
  5. Mar 7, 2008 #4
    Isnt the equation I posted the Biot-Savart law?
     
    Last edited: Mar 7, 2008
  6. Mar 7, 2008 #5

    Doc Al

    User Avatar

    Staff: Mentor

    No. As I said, the equation you posted is the field from a long current-carrying wire. Look up the Biot-Savart law.
     
  7. Mar 7, 2008 #6
    Sorry, about that, I was looking at the wrong equation in my book.

    B = [tex]\frac{\mu_0}{4\pi}[/tex] [tex]\frac{q(v X r}{r^2}[/tex]

    since its circular motion B = [tex]\frac{qmv}{r}[/tex] <=Would I need to ingetrate this equation?
     
  8. Mar 7, 2008 #7

    Doc Al

    User Avatar

    Staff: Mentor

    The one you want is in terms of current:
    [tex]d\vec{B} = \frac{\mu_0 I d\vec{\ell}\times \hat{r}}{4 \pi r^2}[/tex]

    Figure out what that is for a point in the center of the loop, then integrate around the loop.

    Not relevant; No circular motion here.
     
  9. Mar 8, 2008 #8
    Would it be

    [tex]\vec{B} = \frac{\mu_0 I d}{4 \pi r^2}[/tex]

    and then integrate that?
     
  10. Mar 9, 2008 #9

    Doc Al

    User Avatar

    Staff: Mentor

    Almost. After taking care of the vector product, it would be:

    [tex]d\vec{B} = \frac{\mu_0 I}{4 \pi r^2}\;d\ell[/tex]

    Integrate that around the loop. (It's easy!)
     
  11. Mar 9, 2008 #10
    is the [tex]d \ell[/tex] distance*length or the derivative of length.

    Then I would [tex]\oint \vec{B} dr[/tex] like Reshma said?
     
    Last edited: Mar 9, 2008
  12. Mar 9, 2008 #11

    Doc Al

    User Avatar

    Staff: Mentor

    Neither. [tex]d \ell[/tex] is an element of length around the circumference of the circle. (That should tip you off as to what the integral is. :wink:)

    No. Integrate the expression I gave in the last post, which is the field at the center due to a small element of the current, over the complete loop.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Magnetic Field at the Center of a Wire Loop
Loading...