0
$\begingroup$

My book tells me that the arrowhead should point to whichever is responsible for the field.

Am correct in a assuming that it's whichever has the larger mass or bigger electric charge?

$\endgroup$
0

3 Answers 3

1
$\begingroup$

Based on the title of your question, there are only two objects. I'm going to infer that you are analyzing the motion behavior of one of those objects based on the influence of the other. I'm also going to assume that the influence is gravitational and not electrical. That's the context of your question.

You will only show the gravitational force vector acting on the object you want to analyze. It will point toward the other object. It doesn't matter which object has the larger mass.

$\endgroup$
1
$\begingroup$

Gravitational field vectors conventionally are represented pointing toward the gravitating body whose gravitational field is being analyzed. If two gravitating bodies are mutually attracted to each other, and one is in orbit around the other, the center of mass of their system is called the barycenter, and both orbit around the barycenter. This results in an apparent wobble in their orbits, with the star alternately approaching or receding from us, depending on which side of the barycenter it's on. Changes in the star's radial velocity with respect to the Earth as it orbits the barycenter cause a Doppler effect in the star's spectrum, as WhatRoughBeast points out in his comment. That's one way to know if a distant star has planets orbiting around it. Scroll down to the animation in this link: http://spaceplace.nasa.gov/barycenter/en/

Each body's gravitational field is represented by vectors pointed toward itself. The only time you'd use only one vector pointed toward the more massive body is if the less massive has such a weak gravitational field that you choose to ignore it, or if it is a test particle affected by another gravitational field.

Scroll down to the picture of how the gravity fields of the Earth and the Moon are represented in this link: http://www.vias.org/physics/bk4_06_03.html. The vectors represent the gravitational acceleration of a test mass placed in the gravity field.

$\endgroup$
0
0
$\begingroup$

Both objects are responsible for the field, and the total gravitational (or electrostatic) force field is the linear superposition (sum) of the force fields arising from each object on its own. So, for example, if you have two point masses of mass $m_1$ and $m_2$ at positions $\vec{r}_1$ and $\vec{r}_2$, the field at point with position $\vec{r}$ will be:

$$G\,m_1\,\frac{\vec{r}-\vec{r}_1}{|\vec{r}-\vec{r}_1|^3} + G\,m_2\,\frac{\vec{r}-\vec{r}_2}{|\vec{r}-\vec{r}_2|^3}$$

(note the cubic powers in the denominator are needed to represent the inverse square law, since the vectors in the numerators are not unit vectors)

See how the masses naturally "weight" the sum: if one is very much bigger than the other, then the force field will be almost the same as that from the much bigger one alone, aside from in a small region around the smaller mass.

If you plot this out with something like Mathematica, you'll see some very interesting shapes of field lines.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.