Question: The the title is self explanatory, I guess.

Why can two (or more) electric [field lines](http://en.wikipedia.org/wiki/Field_line) never cross?

Answer: 
Electric field lines reveal information about the direction (and the strength) of an electric field within a region of space. 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. Every single location in space has its own electric field strength and direction associated with it. Consequently, the lines representing the field **cannot** cross each other at any given location in space.

For example, in the image below, the lines are intersecting and hence there are **two directions** for Electric Field.

![enter image description here](https://i.stack.imgur.com/qnYkc.gif)
A positive particle accelerates along the electric field lines. If it came to an intersection, what way should it go?