Divergence of a vector field

  • Thread starter jem
  • Start date
  • #1
jem

Homework Statement


I attempted to solve the problem. I would like to know if my work/thought process or even answer is correct, and if not, what I can do to fix it.
I am given:

Calculate the divergence of the vector field :
A=0.2R^(3)∅ sin^2(θ) (R hat+θ hat+ ∅ hat)


Homework Equations


[/B]
The equation I used was the divergence of a vector field in spherical coordinates:
The file is attached:


The Attempt at a Solution


The file is attached:
My final answer is 3.60.
 

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Answers and Replies

  • #2
Ray Vickson
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Homework Statement


I attempted to solve the problem. I would like to know if my work/thought process or even answer is correct, and if not, what I can do to fix it.
I am given:

Calculate the divergence of the vector field :
A=0.2R^(3)∅ sin^2(θ) (R hat+θ hat+ ∅ hat)


Homework Equations


[/B]
The equation I used was the divergence of a vector field in spherical coordinates:
The file is attached:


The Attempt at a Solution


The file is attached:
My final answer is 3.60.
What does your notation mean? What is ##\hat{R}##. What is the difference between ##\theta## and ##\hat{\theta}##, and between ##\phi## and ##\hat{\phi}##? I can guess, but why should I need to, and maybe my guess is wrong. Finally, which of the two common forms of spherical polar coordinates are you using? Some sources use ##\theta## as the polar angle (latitude) and ##\phi## as longitude, while others choose the exact opposite convention. Both appear in this Forum from time to time.
 
  • #3
quiet
Hi. When a vector field is a function of the 3 Cartesian coordinates and time, for example in the case of an electromagnetic wave in a vacuum, can it happen that a divergence of 4 components appears, with the fourth component of the type
[tex]\dfrac{1}{C} \ \dfrac{\partial A}{\partial t}[/tex]
(A symbolizes some field of the wave)
 

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