Calculating divergence as a function of radius

1. Jul 23, 2017

Caleb Jones

{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)
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. Jul 23, 2017

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.

3. Jul 23, 2017

Caleb Jones

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

4. Jul 24, 2017

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.

5. Jul 26, 2017

rude man

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.