Spherical coordinates vector question

In summary, the student is struggling with understanding how to use spherical coordinates in calculating divergence. They attempted to use the formula \nabla . \underline{r} = \frac{1}{r^2}\frac{\delta{r^2}}{\delta{r}} = \frac{2}{r}, but it did not match with the expected answer. It was suggested to use the formula \frac{1}{r^2} \frac{\partial}{\partial r} (r^2 F) instead, where F is the magnitude of the vector function, and to use \textbf{e_r} = \frac{\textbf{r}}{r} for the vector function.
  • #1
renlok
13
0
I've no idea where to put this question but here it is I am trying to work through the examples our lecture has given in class and I wasn't getting them at all
the first thing that confused me was [itex]\nabla . \underline{r} = 3[/itex] I tried this myself with [itex]\nabla . \underline{r} = \frac{1}{r^2}\frac{\delta{r^2}}{\delta{r}} = \frac{2}{r}[/itex] (working in spherical coords)
but if you use [itex]\textbf{e_r} = \frac{\textbf{r}}{r}[/itex] it works but I have no idea where this comes from could someone at least point me in the right direction that would be really helpful thanks

 
Physics news on Phys.org
  • #2
You should try to use the template. But oh well.

You've had a go at using spherical coordinates - yep that's one way to do it. But I think you've done it wrong. When the function is purely radial (as it is in your case), the divergence is equal to:

[tex] \frac{1}{r^2} \frac{\partial}{\partial r} (r^2 F) [/tex]
(where F is the magnitude of the vector function in question). For your problem, F=r.
 

FAQ: Spherical coordinates vector question

1. What are spherical coordinates?

Spherical coordinates are a type of coordinate system used to describe the position of a point in three-dimensional space. They use three coordinates: radius (r), inclination (θ), and azimuth (φ). These coordinates are measured from a fixed origin point.

2. How do spherical coordinates differ from Cartesian coordinates?

Spherical coordinates use a different set of coordinates (r, θ, and φ) compared to Cartesian coordinates (x, y, and z). Spherical coordinates are often used to describe points in a spherical or polar system, while Cartesian coordinates are used for points in a flat, rectangular system.

3. How can I convert Cartesian coordinates to spherical coordinates?

To convert Cartesian coordinates (x, y, z) to spherical coordinates (r, θ, φ), you can use the following equations:

r = √(x^2 + y^2 + z^2)

θ = arccos(z/r)

φ = arctan(y/x)

4. What is the purpose of using spherical coordinates?

Spherical coordinates are often used in science and engineering to describe physical phenomena that involve spherical symmetry, such as planetary motion or magnetic fields. They can also be useful for solving problems involving spherical objects, such as finding the volume or surface area of a sphere.

5. How can I visualize a vector in spherical coordinates?

A vector in spherical coordinates can be visualized as a magnitude (length) and direction in three-dimensional space. The magnitude is represented by the radius (r) and the direction is represented by the inclination (θ) and azimuth (φ) angles. This can also be visualized as a vector pointing from the origin to the specified point in space.

Similar threads

How to define vectors in spherical coordinate system?
Replies
2
Views
795
Integration in polar coordinates
Replies
4
Views
1K
Convert a spherical vector into cylindrical coordinates
Replies
9
Views
2K
Elliptical motion in polar coordinates
Replies
10
Views
729
Height of a stable droplet on a perfectly wetting surface
2
Replies
63
Views
3K
Laplacian in spherical coordinates
Replies
2
Views
2K
Spherical ball rolling back and forth in a bowl
Replies
24
Views
497
Is the Solution for Rotation of Spherical Mirrors Incorrect?
Replies
16
Views
652
Finding the curl of velocity in spherical coordinates
Replies
3
Views
3K
I Dirac delta function in 2d polar coordinates
Replies
4
Views
1K

Hot Threads

Recent Insights

Back
Top