## Homework #2

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## Homework #2

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- Pages:
- 2
- School:
- University of Maryland, College Park
- Course:
- Phys 601 - Theoretical Dynamics

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Physics 601 Homework 2 Due Friday September 17 01 22234 50 67 8 9 0 Hint For some of these problems it will be helpful to use Mathematica or some other symbolic manipulation program If you make use of such a program please 0102 0132 0140 include the output with your homework solutions 01 22234 50 67 8 9 0 5 6 6 7 1 22 2 20 13 4 Goldstein 0102 0132 0140 81 5 9 6 6 9 6 A In5 6 6 7 addition 9 6 A A 6 6 6 96 9 BA 6 1 C 9 2 2 6 A DDD 9 BA 6 81 96 6 6 9 A 6 6 1 E F 2 5 9 6 6 9 6 A G 6 9 H 6 F 696 6 9 6 A A 6 6 6 96 9 BA 6 1 C 9 2 2 6 A DDD 9 BA 6 9 I A 6 6 96 6 6 6 9 A 6 96 6 6 9 A 6 6 1 E F 2 6 1 J 6 9 6 6 6 6 G 6 9 H 6 F 696 6 9 BA 6 6 9 6 96 6 6 6 9 9 I A 6 6 96 6 6 6 9 A 6 6 A 9 6 A A 6 6 1 K 6 6 6 1 J 6 9 6 6 6 6 A A 6 6 A 6 6 1 L 6 D 9 BA 6 6 9 6 96 6 6 6 9 L x y x y 12 m x 2 y 2 12 m 2 x 2 y 2 6 6 69 96 7 6 A 9 6 A A 6 6 1 K 6 6 6 96 6 6 1 A A 6 6 A 6 6 1 L 6 D 2 2 2 1 m x 2y y 212 m x12 2m y 22 x 2 6 9 1 1 2 E L x 12 m y2 x y 2 6 6 69 96 7 2 y x 1 M BA 6 6 6 9 6 96 6 6 1 2 2 22 2 1 1 2 2 12 m x 2 Ey 2 12 m m x y 2 1 BA 6 2 2 x y 2 m 1 x y 2 6 9 1 M BA 6 6 6 9 91 1 9 9A 6 6 2 Q121m 2 x 2L Q y 22 1 BA 6 12 m x 2 y L 6 2 6 Q1 x y Q2 x y 91 9 9A 6 6 x 0 y 0 L Q2 1 y 0 Q1 x y 0 x LQ 2Q x 6 2 6 Q1 x y Q2 x y y 2 6 9 6 6 6 96 6 x y 1 x 0 y 0 Q1 x y 0 x Q2 x y 0 y 2 6 9 6 6 6 1 1 NF 6 9 x 96 6 y 1 1 6 9 BA 6 96 1 NF 6 9 1 A 6 9 6 6 9 6 6 A 1 6 9 BA 6 96 1 A A 6 9 6 6 9 6 6 1 41 O 6 96 A 6 6 6 9 6 6 9 6 AA 41 H 6 6 I 6 6 6 6 9 A 6 6 6 9 9 O 6 96 A 6 6 6 9 6 6 9 6 AA 6 6 A 1 C 6 6 6 A 6 6 H 6 6 I 6 6 6 6 9 A 6 6 6 9 9 6 6 A 1 C 6 6 6 A 6 6 6 6 8 9 6 6 1 P 6 6 6 6 8 9 6 6 1 P 6 6 1 x x ct ct ct x 1 x x ct ct ct x 1 2 2 1 v v 6 96 6 1 C 6 A c 6 96 6 1 C 6 A c 9 6 6 6 D9 P 9 6 x t 6 9 6 6 6 D9 P 9 6 x t 6 0 1 2 x t x t 3 4 5 52 2 0 6 7 8 2 2 527 9 2 527 9 2 2 L 12 t 12 c 2 x 3 5 5 8 2 0 2 S dx dtL 6 8 2 0 1 2 0 2 1 2 272 2 6 7 8 2 t2 c 2 x2 x t 0 93 20 5 52 2 L 2 2 7 2 0 1 0 0 1 L 2 2 2 0 1 3 3 20 2 S dx dtL 2 2 7 2 3 4 2 02 A 92 0 0 1 2 3 3 B 1 3 6 0 1 0 5 52 8 2 2 1 2 0 1 3 20 2 2 3 3 In class we showed that for particles in a magnetic field time independent gauge transformations changed the action for motion between fixed points but did so in a manner independent of the path In this problem you should show it is also the case for particles in an electo magnetic field with time dependent gauge transformations The Lagrangian is L 12 x 2 q x t A x t x and the gauge transformation is given by x t A x t A x t A x t x t x y x t t

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