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I have seen in many books the $2$ dimensional representation of field lines (between two particles having equal positive charge) as-

field lines

But I am trying to visualise this $3$ dimensionally as how the field lines will look if the two positively charged particles are kept in three dimensional vacuum space..which I am unable to.


Can someone help me with this? I am hypothesising that I have to just mentally rotate the image about its symmetrical axis.But which axis? and why? There are two symmetrical axes(one passing through particles and one parallel to them).

Moreover I am also thinking that since lines in field lines are $2$ Dimensional (that is they can only be made in a plane) so maybe it is not possible to visualise this $3$-dimensionally. Is it so?

Does that mean Field lines are not the best way to represent Electric Field beacuse it cannot be visualised 3-Dimensionally?

Can someone please clarify this?

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The electric field lines in 3D are lines and not surfaces and so there is no rotation to be done. I could not find a field line diagram for two charge of the same sign.

enter image description here

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  • $\begingroup$ But Mathematically speaking aren't Lines Two-dimensional so how can we use Theese lines to represent Electric-Field in a $3$-dimensional space ? $\endgroup$ – Freelancer Feb 28 '16 at 7:41
  • $\begingroup$ A line is actually one dimensional? I think that field lines were invented by Faraday who called them lines of force. He used them in an imaginative but imaginary way to "explain" various observations which he had made. He counted the number of lines going through an area and the more lines the stronger the force/effect/field. That is why he used the word flux (=flow). So in the diagram above the electric field is larger near the charges because there are more field lines flowing through an area at right angles to them than if the area was further away. $\endgroup$ – Farcher Feb 28 '16 at 8:18
  • $\begingroup$ @Freelancer: field lines are actually curves, and exist in 3D space. You can visualize them most easily with iron filings and magnets; I like to wrap the magnets so that the I can get the iron off later. $\endgroup$ – Peter Diehr Feb 28 '16 at 12:51
  • $\begingroup$ @Freelancer: the density of the field lines is a measure of the local intensity; the visualization is not perfect. The equipotentials are the surfaces orthogonal to the field lines; these are even harder to draw. $\endgroup$ – Peter Diehr Feb 28 '16 at 12:54

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