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Calculating uncertainty in a experiment

  1. Aug 16, 2011 #1
    1. The problem statement, all variables and given/known data
    Finding uncertainty in magnetic field strength. [itex]N=2[/itex], [itex]i=1.00\pm0.005[/itex] A, [itex]R=0.1[/itex] m, [itex]\tan \theta=0.49\pm0.008[/itex]

    2. Relevant equations
    The equation

    [itex]B_{coil}=\frac{\mu_0 N i}{2 R \tan \theta}[/itex]

    3. The attempt at a solution
    I am assuming that the radius R and number of turns N are exact.
    I know how to find the error when the equation is X=a/b
    Should I find this error and scale it by
    [itex]\frac{\mu_0 N}{2 R}[/itex]?
    Last edited: Aug 17, 2011
  2. jcsd
  3. Aug 16, 2011 #2
    For multivariable formula [itex]y = f(x_1, x_2, \dots, x_n)[/itex]: [itex]\Delta y^2 = \sqrt{\sum_{j=1}^{n} \left( \frac{\partial f}{\partial x_j} \Delta x_j \right)^2}[/itex]

    It looks tedious, but try to work out and simplify the algebra before you plug in number.
  4. Aug 16, 2011 #3


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    Your proposal sounds fine to me.
  5. Aug 17, 2011 #4

    Sorted it out, my problem, I mis-read the formula

    [itex]\frac{\delta X}{X}=\sqrt{(\frac{\delta A}{A})^2+(\frac{\delta B}{B})^2}[/itex]

    For [itex]\delta X[/itex] I needed to have

    [itex]\delta X=\sqrt{(\frac{\delta A}{A})^2+(\frac{\delta B}{B})^2} X[/itex]

    Silly mistake
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