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Why dont electric field lines ever meet?
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If two lines intersect at any point then two tangents can be drawn at one point indicates two directions of electric field, which is not possible because at any point there is only one direction of field. That is why they never cross each other.
by Wooden (1,126 points)
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They will cause two directions  at a point  of intersection. Vector  cannot have two directons
by Wooden (162 points)
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If the lines cross each other at a given location, then there must be two distinctly different values of electric field with their own individual direction at that given location. This could never be the case and hence they could not intersect each other. ... Thus the electric lines of force will never cross each other.
by Wooden (1,121 points)

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