Understanding the Relationship between Electric Field Line Distance and Strength

[FS98]

Supposedly the strength of the electric field is is related to the distance between electric field lines. I have two questions about what exactly this means.

1.) What is the distance between electric field lines? Is it just the distance between two points on adjacent electric field lines that are each the same distance from the charge?

2.) if the distance between electric field lines is twice is great, would it also be true that the electric field must be twice as great in that region, or can you only say that the electric field is largest in that region that one with a smaller electric field line distance? Or in other words, is the distance between electric field lines proportional to electric field strength?

 

[Orodruin]

Supposedly the strength of the electric field is is related to the distance between electric field lines. I have two questions about what exactly this means.

It does not mean anything. It is a colloquial and imprecise expression. It is a useful rule of thumb only if the field lines are drawn in a very particular manner.

 

[jtbell]

if the distance between electric field lines is twice is great, would it also be true that the electric field must be twice as great in that region

Consider a simple point charge. The field lines run radially outwards (or inwards).

1. Does the distance between field lines increase or decrease as you go further from the charge?
2. Does the field strength increase or decrease, as you go further from the charge, according to Coulomb's Law?

 

[tech99]

It does not mean anything. It is a colloquial and imprecise expression. It is a useful rule of thumb only if the field lines are drawn in a very particular manner.

This is one particular manner. When we learned the cgs system of units, we were told that Gauss said 4 pi lines of force are considered to originate from a unit charge.

 

[sophiecentaur]

It does not mean anything. It is a colloquial and imprecise expression. It is a useful rule of thumb only if the field lines are drawn in a very particular manner.

You could say that it is an attempt at an analogue representation of the flux / flux density. It is actually an excellent graphical way of presenting a piece of information that would just not work with any other graphical form or with numbers. 'As far as it goes' it does a great job'.

 

[Orodruin]

You could say that it is an attempt at an analogue representation of the flux / flux density. It is actually an excellent graphical way of presenting a piece of information that would just not work with any other graphical form or with numbers. 'As far as it goes' it does a great job'.

Sure, as long as field lines are drawn in a manner that actually gives that interpretation. My point is that you can choose to draw some field lines arbitrarily close and others arbitrarily far away. It is similar to how you can draw level curves at arbitrary values. You can make those level lines arbitrarily close or far by selecting your levels appropriately. Only when you have equidistant levels is it a good graphical representation of a gradient.

 

[sophiecentaur]

Sure, as long as field lines are drawn in a manner that actually gives that interpretation. My point is that you can choose to draw some field lines arbitrarily close and others arbitrarily far away. It is similar to how you can draw level curves at arbitrary values. You can make those level lines arbitrarily close or far by selecting your levels appropriately. Only when you have equidistant levels is it a good graphical representation of a gradient.

Reading this again, it looks as if you are describing lines of equal potential and not field lines (lines of force). The old, school definition of a magnetic field line is 'the path that an isolated North Pole would take'. There is no mention of actual values and the strength of field is indicated by how close together they are (relatively) over the whole path. Just two lines will give an indication of relative field strength, whatever spacing is chosen at a chosen point.
The lines in the cgs system are another level of sophistication / information which is not usually included in a useful diagram.

 

[FS98]

Consider a simple point charge. The field lines run radially outwards (or inwards).

1. Does the distance between field lines increase or decrease as you go further from the charge?
2. Does the field strength increase or decrease, as you go further from the charge, according to Coulomb's Law?

My bad I meant to ask whether the charge decreased in proportion to distance, not increased. As the distance gets larger, the field strength decreases. What I’m unsure of is whether this decrease is in proportion to the distance increased. If the distance between field lines is increased by a factor of 2, is the force also decreased by a factor of 2?

 

[Orodruin]

Reading this again, it looks as if you are describing lines of equal potential and not field lines (lines of force).

That was a simile. I am saying that the same goes for the field lines. You can choose to draw field lines originating from any two points and they will still be field lines. The trick is to draw field lines with a distance corresponding to the inverse of the field strength along the equipotential surfaces.