Are magnetic fields conservative field?

[fluidistic]

The title says it all. I've heard my professor saying that they are not conservative. I'm very surprised by this. If it is true then I'll think about all the implications it generates.

By the way today was the class where we were introduced magnetic fields for the first time.
Thanks!

 

[Dale]

It seems to me that your professor is getting a little over-technical here, but perhaps he has a reason for making this distinction which will become apparent later in the course.

Energy is definitely conserved in electromagnetic fields (see http://farside.ph.utexas.edu/teaching/em/lectures/node89.html). But technically a magnetic field is not a force field (since the magnetic force also depends on the velocity), so it cannot be a conservative force field. Because the magnetic force depends on velocity you cannot define the gradient of the force, and therefore you cannot set it equal to some scalar function (the potential) as you can with a conservative force field.

 

[fluidistic]

I see, thank you very much.