Editing Magnetic vector potential (section)

=== Example: Solenoid ===
Consider a charged particle of charge <math> q </math> located distance <math> r </math> outside a solenoid oriented on the <math> z </math> that is suddenly turned off. By [[Faraday's law of induction]], an electric field will be induced that will impart an impulse to the particle equal to <math> q \Phi_0/2 \pi r \hat{\phi} </math> where <math> \Phi_0 </math> is the  initial [[magnetic flux]] through a cross section of the solenoid. <ref> {{cite book | last1=Feynman | first1=Richard P. | author-link1=Richard Feynman | last2=Leighton | first2=Robert B. | author-link2=Robert B. Leighton | last3=Sands | first3=Matthew | author-link3=Matthew Sands | title=The Feynman Lectures on Physics | volume=2 | chapter=17 | chapter-url=https://www.feynmanlectures.caltech.edu/II_17.html | publisher=Addison-Wesley | year=1964 | isbn=978-0-201-02115-8 }} </ref>

We can analyze this problem from the perspective of generalized momentum conservation.<ref name=Semon1996 /> Using the analogy to Ampere's law, the magnetic vector potential is <math> \mathbf{A}(r) = \Phi_0/2 \pi r \hat{\phi} </math>. Since <math> \mathbf{p} + q\mathbf{A} </math> is conserved, after the solenoid is turned off the particle will have momentum equal to <math> q \mathbf{A} = q \Phi_0/2 \pi r \hat{\phi} </math>

Additionally, because of the symmetry, the <math> z </math> component of the generalized angular momentum is conserved. By looking at the [[Poynting vector]] of the configuration, one can deduce that the fields have nonzero total angular momentum pointing along the solenoid. This is the angular momentum transferred to the fields.