1. Not finding help here? Sign up for a free 30min 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!

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

    Question:
    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

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

    mfb

    User Avatar
    2016 Award

    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

    mfb

    User Avatar
    2016 Award

    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

    User Avatar
    Homework Helper
    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted