a1010 - stant magnetic ±eld of the form B r = B ˆ z...

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ADVANCED DYNAMICS — PHY 4241/5227 HOME AND CLASS WORK – SET 10 (March 2, 2009) (33) One of the Apollo missions left a mirror on the moon. The McDonald Observa- tory in Texas Fashes a laser wave at this mirror, which is received back after an elapsed time 4 t . At what distance was the mirror, when it reFected the signal? Due March 5 in class (1 point). (34) Let (in arbitrary units) ( a ) ct = 5 , x 1 = 1 , x 2 = 2 , x 3 = 3 , ( b ) ct = 5 , x 1 = 1 , x 2 = 2 , x 3 = 3 , ( c ) ct = 5 , x 1 = 1 , x 2 = 2 , x 3 = - 3 , ( d ) ct = 5 , x 1 = 0 , x 2 = 3 , x 3 = 4 , ( e ) ct = 5 , x 1 = 0 , x 2 = 3 , x 3 = 4 , ( f ) ct = 5 , x 1 = 2 , x 2 = 3 , x 3 = 4 , ( g ) ct = 5 , x 1 = 0 , x 2 = 3 , x 3 = - 4 . Write down the row and column vector for each case and calculate x α x α . Due March 5 in class (7 points). (35) A particle of mass m and electric charge q moves under the inFuence of a con-
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Unformatted text preview: stant magnetic ±eld of the form B ( r ) = B ˆ z . Obtain the most general solution for the velocity v ( t ) using Newton’s second law of motion in combination with the Lorentz force F = m ˙ v = q c v × B . Homework, due March 15 before class (10 points). (36) Consider the 2D rotation ± x 1 x 4 ² = ± cos( φ ) sin( φ )-sin( φ ) cos( φ ) ² ± x 1 x 4 ² and substitute φ = i ζ , x 4 = i x , x 4 = i x . Write out the equations for x 1 and x . Due March 24 in class (8 points). Read the Notes on Relativity up to section 1.1.3 (due March 15)....
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