Prof: You can attend a colloquium ; sleep through the entire session but if you wanted to ask a really intelligent sounding question at the end go with ‘Excuse me, what about the magnetic fields?’ … Works like a charm ! 😀 😀
To understand why this is true, we must start with the Fundamental Theorem of Vector calculus. If is a conservative field ( i.e ), then
What this means is that the value is dependent only on the initial and final positions. The path that you take to get from A to B is not important.
Now if the path of integration is a closed loop, then points A and B are the same, and therefore:
Now that we are clear about this, according to Stokes theorem the same integral for a closed region can be represented in another form:
From this we get that Curl = for a conservative field (i.e ). Therefore when a conservative field is operated on by a curl operator (), it yields 0.
Bravo Prof.Ghrist! Beautifully said 😀
Now flip this over by 90 degree counter clockwise :
Now flip this over again by 90 degree clockwise :