I am recently learning about electric fields. So I encountered the concept of electric field lines. As they are not real but imaginary lines. Why do we need them to understand electric field?

I am asking that we have the equation for intensity $E$ for a point charge is $\vec E=C\frac{Q\vec{r}}{r^3}$. From this, we can know the magnitude and direction of the field at anny point of space, can't I? So why do we need field lines also to understand electric field? Is there any phenomenon or property of electric field that equations can't explain but field lines can. Is there any reason we don't use gravitational field lines?

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    $\begingroup$ Who ever said we need them? Can you cite your source on this? $\endgroup$ – BioPhysicist Feb 13 '19 at 13:03
  • $\begingroup$ @AaronStevens Actually it's not any great physicist but my physics teacher who told me that we need these to understand electric fields easily. But I don't understand how this concept makes things easy. I find this concept rather difficult. $\endgroup$ – Aslan Feb 13 '19 at 15:09
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    $\begingroup$ Your teacher means well. I am probably being a bit nit-picky. I am just saying I can see how you could understand electric field without discussing field lines. Although they are a very useful tool in envisioning the electric field of various configurations. If your teacher wants you to learn it, then you should learn it. And I would argue anyone willing to teach physics is a great physicist in their own way, even if they are not of the same research caliber you usually see in "great physicists" $\endgroup$ – BioPhysicist Feb 13 '19 at 15:15
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    $\begingroup$ That is the point I am making. I don't think it is necessary. I think it is useful, and I think it is worth putting the time in to understand. $\endgroup$ – BioPhysicist Feb 13 '19 at 15:23
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    $\begingroup$ @aslan electric field lines are just a way of representing something that we really cannot see.And there is no need for them in advanced cases because it is not possible to draw electric field lines for complicated charge distributions,so they are of little use,just to indicate there is something present $\endgroup$ – Alfred Mathew Feb 15 '19 at 11:54

If you have a negative electron, then it will attract a positive charge.

  • Put that positive charge above the electron, and it will be attracted downwards.
  • Put it below the electron, and it will be attracted upwards.
  • Put it besides the electron, and it will be attracted sideways.
  • Etc.

Each of these paths that the positive charge would want to move along, is called a field line. Clearly, the electric force direction (the electric field lines) varies with location in the vicinity of the electron. But also the magnitude varies:

  • A positive charge put above the electron is attracted downwards.
  • A positive charge put above, and a bit further away, is attracted less strongly downwards.
  • A positive charge put above, but a bit closer, is attracted more strongly downwards.

When further away, the field lines are farther from each other than closer to the electron. So basically, if you draw many field lines, how closely spaced they are tells us where the electron attracts more strongly. See for example this graphic from Wikipedia:

enter image description here

Closer to an electron, the field lines are closely spaced. But with two electrons put together (left illustration), the paths a positive charge would follow are distorted because it now is attracted towards two points simultaneously.

Or equivalently (right illustration), imagine having an electron and a positive proton in the same vicinity. The electron attracts a positive charge, whereas the proton repels a positive charge - so at a point in between them, a positive charge is both pulled in and pushed in, giving a stronger combined pull and thus closer field lines. The combination of field lines at each point as shown gives us a visual idea of where the attraction is largest and where it is smaller.

All such field lines together (if you imagine drawing up infinitely many of them) make up the electric field.

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  • $\begingroup$ Wait did you just say infinite field line? So the bookish claim that number of field lines produced by a $1C$ charge is equal to $\frac{1}{\epsilon} is wrong? I think it's wrong as it doesn't make any sense. I can always draw some more lines, can't I? $\endgroup$ – Aslan Feb 14 '19 at 3:48
  • $\begingroup$ @aslan Yes, you can always draw more. Can you give an exact quote of what the book says? Sometimes "the number of" field lines is used a bit carelessly or used as a maletaphor for something. $\endgroup$ – Steeven Feb 14 '19 at 5:36
  • $\begingroup$ There's no quote. They just got $E=\frac{\sigma}{\epsilon}$ from coulomb's law. Then told that if $\sigma = 1$ then $\frac{1}{\epsilon}$ is the number of lines. $\endgroup$ – Aslan Feb 17 '19 at 15:48
  • $\begingroup$ @aslan Ah yes, it might have been more accurate to say "line density" rather than "number of lines", but in any case the "number" of lines is just a way to talk about the field strength. If more field lines pass through one square centimeter in one area than in another, then surely that means that they are more compact/more closely spaced there, which means that the field is stronger there. I understand your confusion here, but don't care too much of the exact wording in regard to such words. It is just a way to describe the field. $\endgroup$ – Steeven Feb 17 '19 at 16:41

Understand that at the starting level, especially when students aren't introduced to vectors or their cross products etc., the best way to visualize the direction of the force on charged objects is by electric field lines.

The force experienced by a small positive charge is along the direction of the field (it's in the opposite direction for negative charges). Like if the field lines are curved the force experienced by a point charge on that line is tangent to the field line.

So, combined with Coulomb's Law, with which we can find the magnitude of the electric force, we can use electric field lines (to find direction of the force) to study the electric force.

I'd like to add that for a single isolated charge creating a field, the direction is easy to understand, but fields lines are very useful when dealing with more than one charge, like suppose what would happen if you placed a small positive charge in between two other positive and negative charges as seen in this diagram. Here that small positive charge experiences a force in that direction, tangent to the field.

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Representing and visualizing a spatial field is difficult : you would have to put an arrow on each point of space. Try it with a simple field !

So, you have useful tools to visualize a spatial field. Line fields are one of these tools. They show you the direction of the field and you lose information about the value of the field.

But a lot of information is lost in general with line field : $\overrightarrow{V}=x\overrightarrow{{{e}_{x}}}$ and $\overrightarrow{V}=\sin (ax)\overrightarrow{{{e}_{x}}}$ have the same line fieds !

If the field is divergence free, (with conservative flux) , we know that the norm of the field increases as the lines get closer.

(Sorry for my english)

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  • $\begingroup$ Technically, the distance between lines does give information about field intensity. $\endgroup$ – FGSUZ Feb 13 '19 at 12:03
  • $\begingroup$ If the field is divergence free, it does. $\endgroup$ – Vincent Fraticelli Feb 13 '19 at 12:04
  • $\begingroup$ @VincentFraticelli Sorry if I am being rude. But I didn't understand many things you said. $\endgroup$ – Aslan Feb 13 '19 at 14:01

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