{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# emhw11 - Electromagnetic Theory I Problem Set 11 Due 14...

This preview shows pages 1–2. Sign up to view the full content.

Electromagnetic Theory I Problem Set 11 Due: 14 November 2011 41. In studying a quantum particle in the presence of an electromagnetic field we used the lagrangian L = 1 2 m ˙ r 2 + q ˙ r · A ( r , t ) ( r , t ) (1) When there is time dependence we showed near the beginning of the course that the relation between fields and potentials is B ( r , t ) = ∇ × A ( r , t ) , E ( r , t ) = −∇ φ ( r , t ) A ∂t ( r , t ) (2) a) Show that Lagrange’s equations of motion with this Lagrangian imply Newton’s equation with the Lorentz force on the right side. F = q E + q v × B (3) b) Derive the hamiltonian for this system. c) Repeat the discussion of parts a) and b) for the relativistic Lagrangian obtained by replacing the nonrelativistic kinetic energy term in L as follows 1 2 m ˙ r 2 mc 2 parenleftBigg 1 radicalbigg 1 ˙ r 2 c 2 parenrightBigg (4) 42. J, Problem 5.25. 43. J, Problem 5.32 44. Motional Emf from a Spinning Magnet (Revision of J, 6.4). Let the magnet be a uniformly magnetized sphere of radius R and magnetization M = M ˆ z , which is also a conductor with finite resistivity. Set the magnet spinning with angular speed

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern