1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    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!

Two coils, proving some equations

  1. Feb 9, 2009 #1
    1. The problem statement, all variables and given/known data
    Imagine there are two parallel current-carrying coils, radius R, perpendicular to and centered on the x-axis, with centers at 0.5D and -0.5D. Both carry a current I in the same direction (clockwise). We would like to adjust D so that the magnetic field created by the coils is as constant as possible along the x axis near x=0.

    a) use equation 9.14 (below) to show the first derivative of Bx, with respect to x, is zero for all values of D just because of the arrangement of coils being symmetric about the origin.
    b) If we place the coils a distance D apart, the second derivative of Bx will also be zero at X=0. Find this distance in terms of R.

    2. Relevant equations

    The equation is B=(2*pi*K*I*R^2) / ((c^2 (x^2 + R^2)^1.5))

    3. The attempt at a solution
    I had to derive that from the Biot-Savart law in a different problem. Anyway, if I recall, partial derivatives in respect to say X would be just like treating everything else a constant and X the only variable. In that case, I'd get constant 2piKIR^2/C^2...and then that multiplied by (X^2 + R^2)^-1.5. That derivative in terms of X would be
    -3X / ((X^2 + R^2)^2.5).

    B'=-6piKIR^2/(c^2*(x^2 + R^2)^2.5)).
    A hint is given it might help to argue x should be replaced by X plus or minus 0.5D in this problem...but I don't see where that would help, especially in terms of computing the derivative.
  2. jcsd
  3. Feb 10, 2009 #2
    sorry to pester, but any ideas? thanks.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook