Apologies as this is my first time posting here.
I am trying to simulate Electric Fields and lines of force using pygame to find no flow boundaries. I wrote some crude code and was able to come up with these figures.
What I mean by a no flow boundary, if I put a charge on the line, it moves toward no charge. It will stay and move on the line itself. There exists no flow across the line. Any charge to the left of the line will move towards the left charge and right will move towards the right.
It makes sense cuz the force exerted by the smaller charge will be lower than that of the greater charge at the midpoint, and hence it has to be closer to it to make charges equal. And hence, if we draw the No Flow Boundary on this one, it might look like this.
My question is, how can one figure out where the no flow boundary is; using some vector operation? Is there a way that doesn't rely on looking at field line and then figuring it out? How can I go about "coding" an approximate for the no flow boundary? Is it possible? I feel like it is, cuz we can clearly see it if we plot the lines. Can that feeling be quantified in some way?
I was thinking maybe Divergence, but that just gives me the flow in an infinitesimal area. We know that in the case of the equal charges, the charge might move on the line itself, but never across, so, there will be a non zero divergence on the line.
Any help would greatly be appreciated.