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Biot-Savart law

  1. Nov 18, 2008 #1
    1. The problem statement, all variables and given/known data
    The explanation of this problem is long, but it shouldn't be too hard to solve. I'm just stuck.

    Obtain a symbolic expression for the magnetic field vector B(0,yp,zp) produced at the point (0,yp,zp) by an infinite line current that lies along the x axis. The steady current I flows in the positive X direction.

    It says to use the following method:

    1) Use the vector form of the Biot-Savart law as given in Eqn (29-3)
    [​IMG]
    of the text to write B(0,yp,zp) as a line integral along the entire x-axis. Use the symetry of the problem to convert the integral to twice the integral with the same integrand but now integrated only along the positive half of the x axis as explained on p767. (Basically just multiply by two and do the limits as zero to infinity, correct?)

    2) Express the vector r in unit vector notation and its magnitude r in terms of xp=0, yp, zp, and take coordinates (x,0,0) of ds. express ds as dxi and evaluate the cross product.

    3) Evaluate the resulting integrals using appendix E (integral table) of the text to obtain B(0,yp,zp) in unit vector notation in terms of the givens I, yp, zp.

    To check your solution, use it to find the magnitude of B(0,yp,zp) and compare it with Eqn 29-4
    [​IMG]


    2. Relevant equations
    [​IMG]



    3. The attempt at a solution\

    I think the r for the cross product will be (0,yp,zp). and the ds will be (x,0,0). I'm really lost with this, the cross product integrals are throwing me off. Can somebody get me started? Thanks a bunch.
     
  2. jcsd
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