Evaluate the divergence of the vector field

Click For Summary

Discussion Overview

The discussion focuses on evaluating the divergence of specific vector fields presented in a homework context. The vector fields are expressed in different coordinate systems, including Cartesian and polar coordinates.

Discussion Character

  • Homework-related

Main Points Raised

  • Post 1 presents three vector fields (A, B, C) and requests evaluation of their divergence.
  • Post 2 challenges the correctness of the divergence expression in polar coordinates, suggesting that there are extra factors in the formula compared to Cartesian coordinates.
  • Post 3 indicates that the original poster has made corrections to their work based on feedback received.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correctness of the divergence expression in polar coordinates, as there is a challenge to the original formulation without a definitive resolution.

Contextual Notes

The discussion includes potential limitations regarding the application of divergence in different coordinate systems and the need for careful consideration of the formulas used.

DODGEVIPER13
Messages
668
Reaction score
0

Homework Statement


Evaluate the divergence of the following vector fields
(a) A= XYUx+Y^2Uy-XZUz
(b) B= ρZ^2Up+ρsin^2(phi)Uphi+2ρZsin^2(phi)Uz
(c) C= rUr+rcos^2(theta)Uphi


Homework Equations





The Attempt at a Solution


Uploaded
 

Attachments

  • EPSON014.jpg
    EPSON014.jpg
    10.4 KB · Views: 514
Physics news on Phys.org
Don't know if this post is still important to you since it's a little old, but your expression for the divergence in polar coordinates is incorrect, as there are extra factors in the formula (it's not the same as you would in Cartesian). Take another look at it.

See here https://www.physicsforums.com/showthread.php?t=257816
 
Ok thanks man yah I figured out some of that and fixed it before turning that homework in
 
Cool
 

Similar threads

Calculating divergence as a function of radius
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad What's the physical meaning of Curl of Curl of a Vector Field?
  • · Replies 5 ·
Replies
5
Views
2K
Graduate Vanishing of an integral of a divergence over a closed surface
  • · Replies 1 ·
Replies
1
Views
1K
How Do Killing Vector Fields Form a Basis on S2?
  • · Replies 0 ·
Replies
0
Views
2K
Undergrad Vector field and Helmholtz Theorem
  • · Replies 20 ·
Replies
20
Views
4K
Outward flux of a vector field
  • · Replies 6 ·
Replies
6
Views
2K
Compute the flux of a vector field through the boundary of a solid
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Instantaneous electric field solved by extended electrodynamics?
  • · Replies 1 ·
Replies
1
Views
971
What should I consider when sketching a vector field?
  • · Replies 17 ·
Replies
17
Views
2K
Graduate Divergence of a position vector in spherical coordinates
  • · Replies 24 ·
Replies
24
Views
6K