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Homework Help: Some error calculation help

  1. Oct 26, 2005 #1
    I really struggle with calculating errors :( I understand what i have to do, find the partial derivative of each variable and multiply it by the error, square it, add up all the others then square root the total. I just seem totally incapable of doing it :( The expression i have to find error on is:

    [tex]E = m_{0}c^2 [\sqrt{1+(\frac{RqB}{m_{0}c\tan{\frac{\Theta}{2}}}) ^2} - 1][/tex]

    Where R, B and theta all have errors associated with them!! (to find the error on E)

    I've been told its possible to break it down one bit at a time, so evalulating the RqB bit i get:

    [tex] \sigma = \sqrt{ (B\Delta R)^2 + (R\Delta B)^2}[/tex]

    But no idea where to go next :( Any help much appreciated!
    Last edited: Oct 26, 2005
  2. jcsd
  3. Oct 28, 2005 #2
    So are you having trouble with finding the partial derivatives in the uncertainty expression below??
    [tex]\sigma=\sqrt{(\frac{\delta E}{\delta R})^2*(\Delta R)^2+(\frac{\delta E}{\delta B})^2*(\Delta B)^2+(\frac{\delta E}{\delta\theta})^2*(\Delta\theta)^2}[/tex]
    Last edited: Oct 28, 2005
  4. Oct 28, 2005 #3

    Yeah i was having trouble with it. I think ive solved it now. I went an incredibly long way around it by calling everything else inside the bracket which wasnt the variable to be differentiated, a constant, such as C. That made me see what was going on a bit better and i think it worked! *fingers crossed* i cant change it now as the work has been handed in :) Thanks though!
  5. Oct 29, 2005 #4
    yeah well that's all you do in partial differentiation anyway. You treat everything else as a constant except the variable you are differentiatin with respect to. Then in your case you had to apply the chain rule and bob's your uncle ;)
    Good luck with it then and it sounds like you had the right idea so it should be ok.
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