Calculating Divergence With Spherical Coords

Click For Summary

Homework Help Overview

The problem involves calculating the divergence of a vector field expressed in spherical coordinates. The vector field is given as a combination of unit vectors in spherical coordinates, and the original poster is uncertain about the correct approach to take.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the need for proper notation in vector representation, specifically the use of unit vectors. There is mention of using the gradient formula in spherical coordinates and identifying the functions associated with each unit vector. The original poster seeks confirmation on their progress and whether they are approaching the problem correctly.

Discussion Status

Some participants have provided feedback on the original poster's attempts, noting issues with notation and the need for further expansion of derivatives. There is an ongoing exploration of the correct formulation and understanding of divergence in this context.

Contextual Notes

There is a suggestion that the divergence should result in a scalar quantity, indicating that the original poster may have included unnecessary vector components in their work. The discussion reflects a mix of understanding and confusion regarding the application of spherical coordinates in this problem.

maherelharake
Messages
261
Reaction score
0

Homework Statement



Calculate div v.

v= r sin(θ) r + r sin(2θ) cos(φ) θ + r cos(2θ) φ.


Homework Equations





The Attempt at a Solution



I've never had to do a problem like this using spherical coords, so I am not sure where to start. I have the general formula though.
 
Physics news on Phys.org
What you've shown is not a vector. I'm guessing you omitted putting hats on some of the symbols, like \hat r. But if you have the formula for a gradient in spherical coordinates, just use it. Find the functions in front of \hat r, \hat \theta and \hat \phi and use it.
 
What I have so far is attached (as 6B). Am I on the right track?


http://i77.photobucket.com/albums/j72/maherelharake/photo-25.jpg
 
maherelharake said:
What I have so far is attached (as 6B). Am I on the right track?


http://i77.photobucket.com/albums/j72/maherelharake/photo-25.jpg

Some parts are right. You got some extra hats hanging around. The divergence should be a scalar, right? It shouldn't have any vector parts. And you haven't expanded your derivatives yet.
 
Thank you for responding.
I was still working on it, I just wanted to see if I was on the right track. What about now?
 

Attachments

  • photo.jpg
    photo.jpg
    38.5 KB · Views: 572

Similar threads

Surface area of a shifted sphere in spherical coordinates
  • · Replies 3 ·
Replies
3
Views
3K
Center of mass of spherical shell inside of cone (Apostol Problem).
  • · Replies 3 ·
Replies
3
Views
2K
Can a Vector Field in 3D and Time Have a Fourth Component in its Divergence?
  • · Replies 2 ·
Replies
2
Views
2K
How to calculate a sink using spherical coordinates
  • · Replies 7 ·
Replies
7
Views
2K
Differential Equation: Solving for x in terms of θ | (3+cos2θ)dx/dθ = xsin2θ
  • · Replies 1 ·
Replies
1
Views
1K
Deriving the formula for arc length of a polar function
  • · Replies 4 ·
Replies
4
Views
2K
How do I define a region in R3 with spherical/polar coords?
  • · Replies 3 ·
Replies
3
Views
2K
Triple Integral for Divergence Theorem
  • · Replies 4 ·
Replies
4
Views
2K
Indefinite Integral with integration by parts
  • · Replies 2 ·
Replies
2
Views
2K
Differentiate trigonometric equation
  • · Replies 2 ·
Replies
2
Views
2K