# How to draw the following vector field?

• I
Gold Member
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...

Staff Emeritus
Homework Helper
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2021 Award
That is not a vector field, it is a scalar field. You have no vector in your expression.

Gold Member
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?

Gold Member
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.

Gold Member
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.

Felipe Lincoln
Gold Member
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.

sams
Mentor
2021 Award
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.)

sams and Felipe Lincoln