@MikeyW - Thanks! That really cleared it up for me.
I was looking at the differential equations I had... I just didn't make the connection between them and what I was plotting.
I've seen those differential equations for \textbf{B}. Except in 3D they are three coupled ODE's no? Is there an easier way to solve for the tangent at each point rather than to solve the ODE equations?
Also, I plotted \textsl{B}_{x} vs \textsl{B}_{y}, and it looked like the dipole field...
Okay, right. That makes sense.
I'm attempting to reproduce those plots, in 2D and in 3D, but I still don't fully understand what it means when I plot Bx vs By or Bx vs x vs y (in 3D).
Would Bx vs x vs y represent the gradient of the field in the xy plane?
Well, yes, you have a point. I was just trying to get the picture across of the 'potential to do work' as potential energy. It's not always accurate, but it helped me figure out how to start thinking about it.
To attempt a more precise answer to christian0710's question -
Yes, the electric...
Hi,
I was wondering - In the plots that we see of magnetic lines of force (like this one) what exactly are they plotting against what?
Meaning is it Bx vs x vs y, or is it Bx vs By vs Bz?
Well, you could think of it this way - The electric force is the thing that pushes and pulls the test charge around. Like if you yank a ball on a string, the force of the string pulling the ball is what is moving the ball. The electric potential energy on the other hand, is the energy *possessed...