1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Some math met in EM hw solution

  1. Sep 23, 2007 #1
    I got this :

    1 - z / (R^2 + Z^2) ^1/2 = 1- (1+ (R/Z)^2) ^-1/2
    = 1 - 1 + (1/2) ( R/Z )^2

    I'm confused why it got all these steps. it seems like taylor expansion ? or ?

    Thank you.
  2. jcsd
  3. Sep 23, 2007 #2


    User Avatar
    Science Advisor

    First, it is confusing to me that you are using both Z and z. Are they the same thing?

    I can't speak for WHY they are doing this but how they do the first line is evident: Divide both numerator and denominator of the second term by "z". In the numerator you get z/z= 1, in the denominator the "z" becomes "z2" inside the square root: [itex]\sqrt{R^2/z^2+ z^2/z^2}= \sqrt{1+ (R/z)^2}[/itex]. That is NOT exactly equal to the last line. The last line is an approximation. Yes, you could think of it as a 2nd[/b] degree Taylor polynomial approximation. You could also think of it as a special case of the binomial theorem- extended to fractional powers. Just as (1+ x)n= 1+ nx to first degree, [itex](1+ (R/z)^2)^(-1/2)[/itex] is [itex]1+ (-1/2)(R/z)[/itex]. Of course, now the "1" and "-1" will cancel. To second degree, 1- z/(R2+ z2)-1/2= (1/2)(R/z)2. I assume the next step will involve a limit as R goes to 0 or z goes to infinity or at least that (R/z) is small to make the approximation as accurate as possible.
  4. Sep 23, 2007 #3
    Thank you so much. I got it now.
    btw, could I ask another question that how do you get those words in white block like that ? Thank you. I appreciate it.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook