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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?

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    $\begingroup$ No. They exert equal forces on each other. The force by the first object on the second object points towards the first object (if the force us attractive) and vice versa. $\endgroup$ – march Jul 25 '15 at 21:55
  • $\begingroup$ @march, they are not forces, in the case of electric charge, for negatives, force and field line head in opposite direction.?? $\endgroup$ – most venerable sir Jul 26 '15 at 2:01
  • $\begingroup$ The electric field at some spot in space points in the direction of the force that a positive charge would feel if put at that spot. The E-field of a negative charge points towards the negative charge because a positive charge would feel a force toward the negative charge. But bring in another negative charge and put it at that spot, and it will feel a force in the direction opposite the direction that the positive charge would feel (hence against the electric field created by the original negative charge)... Perhaps I should write an answer... $\endgroup$ – march Jul 26 '15 at 4:03
  • $\begingroup$ @march : I'd be interested to see it, because IMHO the arrowheads on electric lines of force just don't work. Two electrons move apart. Two positrons move apart. One electron and one positron move together. IMHO one has to step up to electromagnetic field interactions to explain how it really works. $\endgroup$ – John Duffield Jul 26 '15 at 9:32
  • $\begingroup$ @JohnDuffield. Am I misunderstanding the question? I'd the OP asking about the total field rather than the field due to just one of them? $\endgroup$ – march Jul 26 '15 at 14:08
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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.

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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.

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  • $\begingroup$ It's not changing intensity that is sensed. As the star orbits the barycenter it will approach or recede (wrt us). This produces Doppler shifts in the star's spectrum, and those are what we detect. $\endgroup$ – WhatRoughBeast Jul 26 '15 at 2:41
  • $\begingroup$ @WhatRoughBeast: Thanks for your correction. I edited the answer to account for the Doppler effect due to changes in radial velocity WRT Earth. $\endgroup$ – Ernie Jul 26 '15 at 6:44
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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.

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