This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Physics 318: Problem Set 3 Due Wednesday, Feb 13, 2008 1. Consider a particle of mass m and charge q acted on by electric and magnetic fields E ( x ,t ) and B ( x ,t ). These fields can be described in terms of the scalar and vector poten tials Φ( x ,t ) and A ( x ,t ), for which E = −∇ Φ − ˙ A and B = ∇ × A . Take the generalized coordinates to be the components ( x,y,z ) = ( x 1 ,x 2 ,x 3 ) of the particle’s position, and take the Lagrangian to be L ( x i , ˙ x i ,t ) = 1 2 m ˙ x 2 − q Φ( x ,t ) + q ˙ x · A ( x ,t ) . a. Show that the Lagrange equations of motion for this Lagrangian give back the Lorentz force law m ¨ x = q E + q ˙ x × B . b. Show that the Hamiltonian H = ∑ i p i ˙ x i − L , where p i = ∂ L /∂ ˙ x i , is H = 1 2 m ˙ x 2 + q Φ( x ,t ) . Note that this differs from the sum T + U of kinetic and potential energies. 2. Consider a system of N particles with positions r n ( t ) for 1 ≤ n ≤ N . Suppose that the system is subject to the holonomic constraints...
View
Full
Document
This homework help was uploaded on 02/24/2008 for the course PHYS 3318 taught by Professor Flanagan during the Spring '08 term at Cornell.
 Spring '08
 FLANAGAN
 mechanics, Charge, Mass

Click to edit the document details