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I read that electric field lines don't intersect. The explanation I was given goes as follows: if it happens then we would have two directions of field.

My question: since field lines are vector, then why couldn't I say that we would have direction according to vector sum? If I am right then what is the correct explanation?

Emilio Pisanty
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super saiyan
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1 Answers1

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The statement that electric field lines do not intersect, since in this case, one would not have a unique direction of electric field, is absolutely correct. The purpose of this electric field line formulation is to indicate the direction of the net electric field at that point in space.

The way out of your confusion is: Imagine any point in space which is exposed to electric field due to two independent sources. One could always construct a resultant as vector sum of the two. In this case, the electric field lines would correspond to this unique electric field strength, not as an intersection of the electric lines of force due to the two sources.

299792458
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  • But why isn't it possible that two electric field lines intersect and have same direction in the intersection point? Like $y=0$ and $y=x^3$ at $x = 0$? – lesnik May 10 '17 at 12:16
  • @lesnik - In the example, the two curves have an identical tangent at $x= 0$, so that takes care of the unique direction of ${\vec E}$ at this one point. The problem would be with the other points in space, everywhere else, there is no such uniqueness. Thus, if these two lines of force were actually originating from two different sources, the strategy would be to add them up and observe the resultant $\vec E$ originating from the resultant. Ultimately, the $\vec E$ originating from a given set of charges (i.e. consistent with given boundary conditions) does have to be unique. :) – 299792458 May 10 '17 at 12:26