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!

Lorrentz force law & vector notation

  1. Aug 22, 2014 #1
    1. The problem statement, all variables and given/known data
    A current element is 3.0mm long, centerd on the origin of cartesian coordinates, and carries a current of 2.5A in the direction ez.
    What field does it produce at the point (3.0, 0, 4.0)


    2. Relevant equations
    This is obviously a Lorentz force law question
    so . . . ∂B = (I ∂I (r-r0)) / I r-r0 I^3

    where B = magnetic field
    I - current
    r - point of origin
    r0 - point being considered


    3. The attempt at a solution
    B = 4∏x10^-7 / 4∏ x 2.5A x 3.0x10^-3 )(ez(3ex + 4ez)) /5^3

    cancelling 4∏'s
    B = 10^-7 x 2.5A x 3.0x10^-3 (ez(3ex + 4ez)) /5^3

    The number bit is easy, but the problem I have is the vector notation.

    Please, how do I do the (ez(3ex + 4ez)) /5^3 bit?

    I have the final answer as
    1.8x10^-11 T ey
    [
     
  2. jcsd
  3. Aug 22, 2014 #2
    I might be missing something, but shouldn't you be considering the Biot–Savart law instead?

    It seems to me like you're being asked to determine the magnetic field produced by a current and not the force on a point charge in an EM field.

    Edit: I see hints of the Biot–Savart law in your expressions, so I guess it was just a typo.

    If you start out with the differential:
    [tex]
    d\mathbf{B} = \frac{u_0}{4\pi}\frac{I d\mathbf{s}\times \mathbf{\hat{r}}}{r^2}
    [/tex]
    where ##d\mathbf{s}## is directed along the current and ##\mathbf{\hat{r}}## is a unit vector towards the point you're considering.

    Then since ##d\mathbf{s}\times \mathbf{\hat{r}}## is always directed along ##\mathbf{e}_y##, you have:
    [tex]
    d\mathbf{B} = \frac{u_0}{4\pi}\frac{I |d\mathbf{s}\times \mathbf{\hat{r}}|}{r^2}\mathbf{e}_y
    [/tex]
    The problem is then to find expressions for ##d\mathbf{s}## and ##r## in terms of a common variable you can use to integrate over the whole of the current element.

    Any help?
     
    Last edited: Aug 22, 2014
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted