How to draw the following vector field?

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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
Orodruin
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That is not a vector field, it is a scalar field. You have no vector in your expression.
 
  • #3
Felipe Lincoln
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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
Felipe Lincoln
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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
sams
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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
Felipe Lincoln
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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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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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