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The meaning of the delta dirac function

  1. Jan 29, 2013 #1
    1. The problem statement, all variables and given/known data

    For a function ρ(x,y,z) = cδ(x-a), give the meaning of the situation and describe each variable.

    2. Relevant equations

    As far as units go, I know that:

    ρ(x,y,z) = charge density = C/ m^3
    δ(x-a) = 1/m
    and if those two are correct, then b must have units of (C/m^2), which is some sort of surface charge distribution.

    3. The attempt at a solution

    I'm new to delta dirac functions and my understanding is very superficial. When the function is not inside an integral, I especially don't understand it!

    I think that "a" represents some sort of center point where there is infinite charge density, and x is the distance from the center.

    Any guidance would be greatly appreciated.
     
  2. jcsd
  3. Jan 29, 2013 #2

    tiny-tim

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    hi anban! :smile:
    no, x is one of the three coordinates, (x,y,z)

    hint: describe where is δ(x-a) ≠ 0 ? :wink:
     
  4. Jan 29, 2013 #3
    I'm not sure that I understand-- does δ(x-a) ≠ 0 when x=a?

    The way I am thinking about this now is that x-a is some coordinate point along a line?
     
  5. Jan 30, 2013 #4

    tiny-tim

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    eg hi anban! :smile:

    (just got up :zzz:)
    your mathematical language is rather strange :redface:

    x-a is just an expression, you need to put it in a sentence

    eg x-a = 0 is the whole plane x = a,

    ie the points (a,y,z) for any values of y and z :wink:
     
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