Why don't electric field lines cross each other?

Answer 1

Actually they can, the effect of which is what causes the Sun to go through its heightened active phase every 11 years. Basically the Electromagnetic field lines get wrapped all around each other since the equator of the sun spins much faster the the poles. This causes all the Coronal Mass Ejections, massive sunspots, and most of the Suns activity during its peak periods...check out the video at the link below for a vid of the field lines getting all whacked out.

Answer 2

The E field lines represent the forces on a test charge if it was placed there. Electric, gravitational and magnetic fields are "uniquely" defined and are continuous once the source(s) are fixed. If you have 4 masses arranged at the corners of a square, the gravitational fields are known and not cross. Unique means a test body will only follow a unique trace of motion along the line. Continuous means there are no sudden breaks or more than one choices. Crossed lines would mean the point of interaction not be unique and continuous.

Answer 3

They aren't "real" lines in any sense. When you see them drawn as lines, that's meant to be an illustration to help you understand. Nothing more.

Suppose, for example, a map were drawn of the US, and arrows fanned out from Chicago showing the most direct route to a bunch of other cities. Those arrows would never cross (else something wouldn't have been the most direct route). It's the same idea with electric field "lines". Them not crossing is part of the definition/concept.

Answer 4

If they did, objects under their influence would not "know" what direction to move in. Since they can only move one way, the lines do not cross.

Answer 5

You are asking questions similar to what Gauss and Faraday asked. The simple answer is because their magnetic components repel one another. A more complex answer can be found below. The second link is a simulator to let you play with some of the ideas.