On 8/23/2003 12:18:14 PM, abk511 wrote: >how do electric field lines >never cross?
Think of it this way. Consider that each point has a "direction." This direction is the direction of force if a proton (not an electron - that would be opposite) were placed at that point. If I place a point on one of the curves, the point will start moving along that curve.
Now, consider what it would mean if two of these curves intersected. There would be a point (the intersection) with more than one direction. This would be like you running in two directions at once.
It is important to note that these lines can "intersect" in a way. However, the intersection is an equilibrium point (stable or unstable). At these points, the magnitude of the net force is zero, so the direction of that force does not really matter. If you have two identical charges, the midpoint between them will be like this. In this case, it is unstable (the slightest nudge to either side would send a particle flying away). Consider that I put an identical charge on the corners of a cube. The center of the cube is an intersection point. This time, however, it is stable. Slight nudges will push the point off, but that point will return to its original position.
Now, back to the point about the field lines. Consider that I do this: Pick a point. Find the direction of the force at that point. Move a tiny increment in that direction Repeat from this point.
As the increment becomes very, very, very small, the path you end up following is a field line. What happens if you encounter an intersection? You get stuck.