I have a doubt about the electric field lines for a continuous distribution. Well, if there's only some point charges, I know that the field starts on the positive ones (or at infinite), ends at negative ones (or at infinity) and the number of lines is proportional to the number of charges. That's fine, but what are the "instructions" to draw the field lines when the distribution is continous ?

I've seem some places where they draw the lines just imagining that the continuous distribution is the same as a finite distribution of small charges $dq$, but I'm not sure that this is the way to do it.

Can someone point out how do we work with this ?

Thanks in advance!

  • $\begingroup$ Are you asking what the electric field looks like within the distribution, or outside of it? $\endgroup$ – Ataraxia Mar 24 '13 at 19:44
  • $\begingroup$ Sorry, I forgot to point this out, I'm thinking outside of it. My problem is: when using Gauss' Law I need to know the direction of the field, so I need the field lines, but I'm confused how to work with it for continuous distributions. $\endgroup$ – user1620696 Mar 24 '13 at 20:00
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    $\begingroup$ The directions of the electric field lines from continuous charge distributions are only easily expressible in cases of high symmetry (e.g. only in a particular region of space), or if it is an infinitely large distribution (e.g. an infinitely long cylinder, or an infinitely long sheet). $\endgroup$ – sujeet Mar 24 '13 at 21:36

From your comment, it seems you want to know how to determine the direction of the electric field of a continuous charge distribution at points not in the charge distribution when you are applying the integral form of Gauss's law to obtain the electric field.

The procedure commonly used to obtain the electric field using Gauss's law for continuous charge distributions relies on the fact that the distribution possesses some symmetry. In particular, the procedure is commonly applied to distributions that are either spherically symmetric, cylindrically symmetric, or possess 2-dimensional planar symmetry.

In each of these cases, it is possible to determine the direction of the electric field before attempting to apply the integral form of Gauss's law to determine the magnitude of the field. In fact, there is a theorem on can prove which shows that if the charge density possess a certain symmetry, then the electric field must also respect that symmetry.

It follows, for example, that in the case of spherically symmetry, the electric field must point radially because only radially pointing vector fields are invariant under all rotations just as the charge density is.

Similar statements hold for charge distributions enjoying other symmetries.


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