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Calculating divergence as a function of radius

  1. Jul 23, 2017 #1
    {Moderator note: Member advised to retain and use the formatting template when starting a thread in the homework sections}

    Hey guys

    Calculate the divergence as a function of radius for each of the following radially
    symmetrical fields in which the magnitude of the field vector:
    (a) is constant;
    (b) is inversely proportional to the radius;
    (c) is inversely proportional to the square of the radius;
    (d) is inversely proportional to the cube of the radius.

    Im completely stumped on this question...
    What I've got so far: (None of this was provided in the question)
    Radial field:
    V = 1/r2 (Vector "r")
    Divergence of a spherical Shell:

    div F = ∇⋅F

    Flux through a spherical shell:
    ∅ = ∫ E.dA ---> E Constant
    ∅ = E ∫ dA
    ∅ = E×4(pi)×r2

    Im not sure if I'm on the right path here though

    Last edited by a moderator: Jul 23, 2017
  2. jcsd
  3. Jul 23, 2017 #2


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    Staff: Mentor

    That is a scalar field, not a vector field. A vector field could be ##\vec F = \vec r##, for example.
    You'll have to find the correct fields first.
  4. Jul 23, 2017 #3
    Thank you mfb
    How do I find these fields?
    Can I just use any symmetric field?
    Sorry for my lack of knowledge, this hasn't been explained in lectures or in our lecture notes
  5. Jul 24, 2017 #4


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    Staff: Mentor

    You'll need a field that is (a) constant with r, (b) inversely proportional to the radius, and so on. The field I gave as example is proportional to the radius.
  6. Jul 26, 2017 #5

    rude man

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    Gold Member

    Follow post #4 to get your 4 fields. His example (field proportional to r) could also be written F = k1 r with r as the unit vector so Fr = k1 where F = Fr r.

    What is the expression for ∇⋅ F for cylindrical coordinates? Look it up most anywhere. Rest is a gimme.
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