Consider an electric dipole consisting of charges $-q$ and $+q$, separated by a distance $2a$ and placed in free space. Let $P$ be point on the line joining the two charges (axial line) at a distance $r$ from the centre of $O$ of the dipole.
You can observe in the above figure that electric field has two directions at the same point $P$, does this mean electric field lines of two charges can intersect?
This is the common figure given in all text books, what I can observe is that field line due to $+q$ charge ends at $-q$ charge and then it doesn't progress towards the point $P$, and nowhere I see the lines of $+q$ and $-q$ intersecting, now I can't conclude that field lines do intersect. So, does field line concept explain electric field due to electric dipole?
What I observed in Wikipedia dipole page is that, axial line is only vanishing!
Sometimes I might have misunderstood the concept, if so pardon me and explain.
Best Answer
If you take a permanent magnet, and place a sheet of paper over it. Now sprinkle iron filings on it, and you pretty much get this diagram. This has been the mainstay of field theory since Faraday's time.
A test charge at rest will begin to move in the direction of the field line. Since there is nowhere that it can rest where there is more than one possible direction of motion, there must be no crossings of the field line.
The line that disappears to infinity in one way, and reappears from the other side, means simply that the flux is moving on ever-large circles, and that in the axis-line of the dipole, it is feeding flux as a stream through it. But all this means is that it is turning something that is already there, but never getting a full rotation of the disk up.
In the real world, these polar flux lines simply wander off to another electrical system. Gauss's flux law says that there is a sphere with a net flux across it equal to the enclosed charge: a net of zero does not mean everywhere zero.