# Confusion In Terminology of Electric Field Lines

I learned about Fields in physics from this video, and i concluded that the concept of field is a theory.

I am going to focus on electric field and how i think it works. 'A charged particle creates a big Ripple on the field and due which the other charged particle gets repelled or attracted'. I hope this is correct because this is what i concluded after learning about fields and my question is also based on this guess.

But as i went further in my chapter(Electrostatics) i got confused as it said that Electric Fields are inversely proportional to the square of distance between the charges(r^2).How is this possible?, shouldn't the correct word be "The effect/ripple by a charge on an electric field is inversely proportional to square of the distance between them" and NOT "Electric Field is inversely proportional to the square of distance between the charges" ?.

Furthermore, the book also says "Electric Field Lines OR lines of electric force". So i think it is quite clear that the lines or arrows are for the ripple created on a field,right?.

You are confusing a couple of things (not by your fault, when introduced to vague definitions, everyone gets confused).

The definition of a field is a function of position in space which returns a number (in which case it is called a "scalar field") or a vector (then it is called a "vector field"). For example, temperature is a scalar field - to each point in space you can assign a number, its temperature. The velocity of the air in the atmosphere is a vector field: to each point you can assign a velocity vector which describes the direction and magnitude of the air velocity at that point.*

Imagine a configuration of electric charges in space. If you try to put somewhere another charge, it will feel a force due to the electrostatic forces from all of the other charges. However, this force is linear with how much charge you put in that point, so one can define the force per unit charge as a certain property of that point. What I want to say is, that you can assign to each point in space the force a stationary electric charge would feel if you placed it in that point (per unit charge). This is the definition of the electric field, a function which assigns to each point in space a vector (that's why it's a vector field).

Because the electrostatic force between two charges falls off like the distance squared, by definition, the electric field from a charged particle will fall as the distance squared.

So what is it with all that rippling? It is more advanced, but when an electric charge will start accelerating, it changes its distance to other points in space, meaning the electric field will need to change due to its movement. It turns out however, that this doesn't happen immediately. This is similar to throwing something into a bath-tub, the water level should rise - but the edge of the bath doesn't immediately increase when the object enters - there is a "ripple" of information telling the water far away that something changed. So when a charge starts moving, there is a "ripple" in the electric field telling it to update to the value it should be now because the charge moved. This should give you a more correct intuition to what's going on. The truth is a bit more complex, but you'll see when you finish your course in electromagnetism (and the second part of the last word is a hint to what I didn't tell you).

About field lines - it's a nice way to represent vector field, so it's quite useful. It's just a way to represent the vector field instead of drawing a lot of arrows.

• Footnote: In both examples these fields aren't well defined in a microscopical level, you can't really assign a value to velocity of air when you're looking a resolution of 10nm for example. These fields are well defined on a "coarse-grain scale". The electric field, however - is well defined on each scale (until you get to the plank scale which is 20 orders of magnitude smaller than a width of a proton, so for all practical purposes - it is well defined.
• This really cleared every doubt I had about electric field, thanks. Apr 13 '20 at 3:57