Question

what is the meaning of streamlines in electric field

Answer 1

Streamlines are the flux lines or the lines of the electric field. If you have an isolated point charge in space, the electric field is directed radially away from it. If you sample a lot of points in space around the space charge and draw vectors representing the E field at those points you get something like the left part of the drawing below.



Sorry, it's a poor drawing. Those line segments are vectors directed away from the +Q charge as the E field is pointing away from the charge. The vectors get shorter as 1/r^2 the further away from Q that you get. If you make a lot of samples in space, you can begin at the charge Q and draw a line parallel to the E field a shown in the diagram at the right. The lines are in the same direction as the E field at every point. If you had a *massless* positively charged particle and released it from rest at some point on one of those lines, it would accelerate out to infinity following the line. Once you add mass, there is inertia and although the particle will experience force in the direction of the line, an initial velocity not parallel to the line will mean the particle will not move along the line.

Those lines are the flux lines or streamlines. They are not really "E-lines" as I have called them because although they contain the directional information of the E field at every point on them, they don't contain any information about the field strength. One thing you should note is that those lines can never cross. If that was the case, then at the point where they cross, you would be claiming there was two directions of the E field which is not possible. So, these streamlines never cross and you will note that if you start with a fixed density of lines along the perimeter of the charge, the lines will spread out as they grow distant from the charge. This spreading out corresponds to the field weakening so you can also say the density of flux lines corresponds to the E field strength.

There is much more to it though -- the density of flux lines exactly reflects the field strength. This comes about from Gauss's Law which makes the connection between flux lines and field strength.

The +Q charge shown in the diagram could just as well have been a -Q charge, in which case the flux lines would be directed toward the -Q charge. So +Q charges act as sources of flux lines (lines move away) while -Q charges act as sinks (lines move toward them). In a complicated configuration of charges in space, these flux lines will always move away from a + charge and terminate on a - charge.