How to draw the following vector field?

In summary, the conversation was discussing how to draw a vector field represented by the function F(r) = 1/(r^2), which was initially mistaken for a scalar field. The correct expression is F(r) = 1/(r^2) * r-hat, and it was suggested to draw the field by attaching arrows at sampled lattice points with length r^-2 pointing towards the origin.
  • #1
sams
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How to draw the following vector field:
F(r) = 1/(r^2)

I know the shape of this vector field and how to draw a vector field in terms of x- and y-components, but I was wondering how to draw a vector field in terms of a vector r, as given above, without knowing its components.

Any advice is much appreciated! Thanks a lot...
 
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  • #2
That is not a vector field, it is a scalar field. You have no vector in your expression.
 
  • #3
Orodruin said:
That is not a vector field, it is a scalar field. You have no vector in your expression.
Isn't it a vector field ##f:\mathbb{R}^1\to\mathbb{R}^1## with one-dimensional vectors along the x axis?
 
  • #4
Well, in fact it isn't a vector field. Maybe if you have written is as ## \vec{F(\vec{r}}) = \dfrac{\vec{r}}{r^3}## it'd be the way I though at first.
 
  • #5
Orodruin said:
That is not a vector field, it is a scalar field. You have no vector in your expression.

I corrected this vector field (excuse me for this mistake):
$$F(\vec{r}) = \frac {1} {r^2}\hat{r}$$

I was wondering how to draw this vector field.
 
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  • #6
Right, now it represents a vector field.
Imagine this way. You have this force, so every position ## r## that some body is, it'll have a well defined vector that represents the force the body will feel. So if you let ## r## be arbitrary, you have a vector field, that represents in some way "each vector of every point" in the one-dimensional coordinate, which is your case.
 
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  • #7
sams said:
I corrected this vector field (excuse me for this mistake):
$$F(\vec{r}) = \frac {1} {r^2}\hat{r}$$

I was wondering how to draw this vector field.
E.g. take the lattice points (points with integer coordinates) around the origin as samples, since you cannot draw the field at every possible point. Now you attach an arrow at this point ##r##, which has length ##r^{-2}## and points toward the origin, as ##\vec{r}## points there. (Or the other way around, depending on whether it is an attractor or repeller.)
 
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1. What is a vector field?

A vector field is a mathematical concept that assigns a vector (such as an arrow) to each point in a given space. These vectors represent the direction and magnitude of a physical quantity, such as force or velocity.

2. How do I draw a vector field?

To draw a vector field, you first need to understand the function or equation that defines the field. Then, you can plot points on a graph and draw arrows at each point to represent the direction and magnitude of the vector at that point.

3. What tools do I need to draw a vector field?

You can draw a vector field using a variety of tools, including graphing calculators, computer software, or even just pen and paper. Some tools, such as graphing calculators, may have specific functions or features that make drawing vector fields easier.

4. How do I determine the direction and length of the arrows in a vector field?

The direction of the arrows in a vector field is determined by the function or equation that defines the field. The length of the arrows represents the magnitude of the vector at each point. You can use a key or color-coding system to indicate the specific direction and magnitude of the vectors in your drawing.

5. Can I draw a vector field in three dimensions?

Yes, it is possible to draw a vector field in three dimensions. This may require using more advanced tools, such as 3D graphing software, and may be more complex than drawing a two-dimensional vector field. However, the concept remains the same - assigning a vector to each point in a given space.

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