Magnetic Vector Potential Around a Wire Carrying Current

[snoopies622]

Until about ten minutes ago I had never heard of the magnetic vector potential $$\vec A$$, defined such that

$$\vec B = \nabla \times \vec A$$.

I am having trouble visualizing this. What would the magnetic vector potential field look like around a straight wire carrying a (constant) electric current?

 

[atyy]

Try Eq 324, 325 from Fitzpatrick's http://farside.ph.utexas.edu/teaching/em/lectures/node38.html. The magnetic vector potential is not unique, and Fitzpatrick states the gauge condition for Eq 334 in the final paragraph.

 

[snoopies622]

Thanks atyy, that's a great reference.

 

[snoopies622]

Follow up:

Is the Lagrangian of a charged particle in an electromagnetic field

$$L = \frac {1}{2}m( \dot x ^2 + \dot y^2 + \dot z^2 ) - q \phi + q (\dot x A_x + \dot y A_y + \dot z A_z) ?$$

(I'm not sure if that should be $$-q \phi$$ or $$+ q \phi$$.) If so, is this good for both static and changing EM fields?

Edit: oh wait, here it is. Equation 1.34. at

http://www.ks.uiuc.edu/Services/Class/PHYS480/qm_PDF/chp1.pdf

All set, then.