Understanding field representation of force

[Anupam]

I am reading the book "The Evolution of Physics". I have a doubt in the topic "The field as representation". In this topic authors give the example of gravitational force represented as a field. In the following image the small circle represents an attracting body(say sun) and the lines are the well known lines of force of the gravitational field.
Image
It is said that the density of the lines of force in space shows how the force varies with the distance. Let us consider a finite volume ΔV in the vicinity of sun. Now the number of lines of force passing through this is finite but there are infinite points in this ΔV volume.
1.Is there any gravitational force acting on those points through which no line of force passes.
2. If the gravitational force acts on all the points contained in ΔV shouldn't there be infinite lines of forces passing through ΔV.

3. If it is supposed that there are really infinite lines of force passing thru ΔV then how to decide the density of no of lines won't it be infinite.
NOTE: "_lines of force_" and "_Field_" these two are synonymusly and interchangably used in the mentioned book.
Please cite some canonical references which explains the 3 different points i mentioned in your answer.

 

[Legaldose]

Gravity doesn't just happen along those specific field lines. It permeates through all space continuously. What that drawing is telling you is that the density of the lines is related to the strength of the field. It's simply a visual aid, you can't make any direct calculations from it.

1. Yes, because a field, by definition, is continuous.
2. Technically, yes.
3. That's precisely why they don't draw an infinite number of lines. The idea is to give you a visual aid.

Read this: http://en.wikipedia.org/wiki/Field_line

 

[Anupam]

@Legaldose you are using a different terminology. In the book [here](https://archive.org/details/evolutionofphysi033254mbp) the authors use the term "field" and "field lines" synonymously. It is the field lines which are in brief called the field. Field is just a representation. If you say field is continues than you will have to say "field lines" are also continues. "Field lines" are not a map of "field". "Field lines" are the "Field".
I have another question related to this post should i ask as a new post or should i post it here in this current post.

 

[sophiecentaur]

I
1.Is there any gravitational force acting on those points through which no line of force passes.

Field lines are only a representation. The sort of field we deal with in Physics is continuous from location to location. The lines show the direction and the density of the lines indicates (only indicates) the amplitude. You would never do a calculation on the basis of the lines.

Magnetic field lines are even more confusing in regions where two N poles are close together. Also, those pesky iron filings can really mess up your understanding of the true shape of fields in places. It's a good thing we don't have the gravitational equivalent to iron filings! :big grin:

PS It is quite reasonable to be at odds with some of the things you can find in textbooks - especially when they are trying to be 'chatty' and to make a topic approachable. They can often over-egg that and give a wrong impression.