PHYSICS 131 Final2008

# PHYSICS 131 Final2008 - FINAL EXAM, PHYSICS 131, Jun 6,...

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FINAL EXAM, PHYSICS 131, Jun 6, 2008 Instructor: Anthony Zee TA: Kevin Moore Please hand your completed exam to Kevin Moore at 5 PM on Monday . Alternatively, you may email a completed exam to him, or place your exam in a sealed envelope and place it in his mail box. You may consult your own class notes, the text by Hartle and the homework solutions. Do not use other texts or computer algebra systems like Mathematica, Maple or the “symbolic solvers” provided by some graphing calculators. Assume unless otherwise noted that G = c = 1, and that Greek indices μ, ν, . . . run from 0 to 3 while Roman indices i, j, . . . run from 1 to 3. Problem 1. The torus, or the two-dimensional surface of a donut, has its line element given by ds 2 = a 2 2 +( b + a sin φ ) 2 2 where a and b are two constants that have dimensions of length and satisfy a < b . (a) 5 points Sketch the surface, and identify a , b , θ and φ on it. (b) 5 points Calculate the ChristoFel symbols. Hint: most of them vanish.

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## This note was uploaded on 07/15/2008 for the course PHYS 131 taught by Professor Kevin during the Spring '08 term at UCSB.

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PHYSICS 131 Final2008 - FINAL EXAM, PHYSICS 131, Jun 6,...

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