Thanks. I realized 1 was very dumb after remembering what conservative and close integral meant.
Additionally, even I'm not sure what I'm asking or saying for 2
Yes, I'm trying to highlight two points of confusion. You're right I was not clear enough. I hope this helps.
1) I am asking why B-fields do no work on a point charge when the path integral of a charge on a B-field is non-zero? Did we define work as path integral only over conservative fields...
This statement has always confused me. Now my confusion is coming home to roast while we cover EMF.
If we consider work mathematically as ∫f.dl and require integral to be path independent then of course the B-field does no work.
However, it seems like there is a deeper meaning to B-fields do...
Wow! I have no idea how I missed that! That raises a different question though. If we have EQ 7.18 from section 7.2.2, then why in the solutions does Griffiths find phi first when EQ 7.18 only requires partial of B. Do I need to find phi?
Ok, so I understand how to find dphi/dt that is integral of -d/dt(B "dot" da). In this case I find a Phi that is a constant in space in time which causes me confusion in next step.
Edit: dphi/dt is constant...
Grithff's then says E field same as a Mag field above center of circular current. He...