# Variation in electrical lines of forces with intensity.

1. Apr 5, 2009

### dE_logics

This is what a book says -

“The number of lines per unit area through a surface perpendicular to the lines is
proportional to the magnitude of the electric ﬁeld in that region. Thus, the field
lines are close together where the electric ﬁeld is strong and far apart where the
ﬁeld is weak.”
+
“These properties are illustrated in Figure 23.20. The density of lines through
surface A is greater than the density of lines through surface B. Therefore, the magni-
tude of the electric ﬁeld is larger on surface A than on surface B. Furthermore, the fact
that the lines at different locations point in different directions indicates that the ﬁeld
is nonuniform.”

What I concluded from the above -

That means the total intensity of E.F passing though an area is independent of the number of lines of force, depends more its density and is directly proportional to it.

So even if we are comparing 2 areas having areas A and 2A and suppose x lines of forces passes through them so the total intensity of the field at A should be greater than 2A, if the areas are charged partially, then the force on A will be more than 2A despite the fact that the number of lines of forces passing through both of them are the same the E.F on A will be higher cause the density of the lines are A is higher.
Talking about insane analogies, Suppose we have 2 area A and 500k A, and if the density of the lines in A is more than 500k A, even though the difference is very less A will get more E.F and so if the areas are charged, A will generate more attraction relative to 500k A, even though the number of lines of forces passing through 500k A is like 490 times of A.
So what final conclusion we have here is that from where the lines of forces pass, it just means that an E.F is present there and does not has to do with the intensity; only the density of lines has to do with the intensity.

Considering the above, suppose we have 2 areas -

http://img223.imageshack.us/img223/5449/2areas.jpg [Broken]

Then even if the small area is one trillionth of the larger area, it will experience more force.

Well...sounds insane to me.

Now following Columb's law the density of lines of forces should decrease with distance, however major ambiguities come by when considering the geometry, you see when comparing a point charge and a plate, the density decrement per unit space of the point charge will be more than the pate; considering this r2 relation should not be applicable to the plate.

And finally what do you mean when one line of force passes through an area?...I mean the ield at this state should have a minimum possible value, but still needs to decrease with an inverse square relation to distance...what will happen then?

Last edited by a moderator: May 4, 2017
2. Apr 5, 2009

:grumpy:

3. Apr 6, 2009

### dE_logics

I got my exams people!

I cant leave this chapter!...my course basically is comprised of DC circuits...which's done with ease, EM and AC.

I was panning to leave EM considering the nature of my problems, but Ineed that while doing AC.

The 'inductance' crashes all plans!

4. Apr 6, 2009

### dE_logics

And this is exactly the problem where I left.

5. Apr 26, 2009

### dE_logics

Still no responses?

6. Apr 26, 2009

### f95toli

I am not sure I understand your question.
But, you DO understand that the lines are not actually "real" in any way, don't you?
They are mathematical constructs that are used to show what the field "looks" like (i.e. how it would affect point charge); they are no more real than the contour line you will find on maps that are used to illustrate the topography.
Hence, the "scale" (total number of lines) for any given picture is arbitrary; it is the DENSITY of the lines that tells you where the field is strongest but that will be true whether you are using 10 or 100 lines.