2061x2_solutions_fa02

2061x2_solutions_fa02 - PHY2061 R. D. Field PHY 2061 Exam 2...

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PHY2061 R. D. Field Exam 2 Solutions Page 1 of 8 November 12, 2002 PHY 2061 Exam 2 Solutions Problem 1 (20 points): Circle true or false for following (2 points each). (a) (True or False) The speed of light in a vacuum is independent of the velocity of the source of the light, but depends on the velocity of the observer. (b) (True or False) The magnetic force cannot change the direction of a charged particle. (c) (True or False) The magnetic field produced by a charged particle is perpendicular to the velocity of the particle. (d) (True or False) The magnetic force on a charged particle is perpendicular to the velocity of the particle. (e) (True or False) The mass of a charged particle depends on its speed, but the ratio of its electric charge to its mass is independent of the particles speed. (f) (True or False) There can be no electric or magnetic force on an electrically neutral wire. (g) (True or False) The kinetic energy of a particle with non-zero rest mass, m 0 , traveling at a speed of 2.598x10 8 m/s is ( approximately ) equal to its rest mass energy. (h) (True or False) The vector function y x x y y x B ˆ ˆ ) , ( = r represents a possible magnetic field in a vacuum with magnitude given by 2 2 ) , ( y x y x B + = . (i) (True or False) The total net magnetic flux through any closed surface is always zero. (j) (True or False) Light has no mass and no momentum but it has energy.
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PHY2061 R. D. Field Exam 2 Solutions Page 2 of 8 November 12, 2002 Problem 2 (relativity, 20 points): Two particles with charges + Q and -Q are at rest in the O'-frame (particle frame) a distance y' = d apart as shown in the figure . The two particles are moving with a constant speed V = 0.9c in the x-direction in the O-frame (lab frame). ( Do this problem relativistically correct! ) Part A (4 points): Which of the following gives the electric force that the -Q particle exerts on the +Q particle in the particle frame ? ( circle one answer and show your work ) (a) y d KQ ˆ 2 2 (b) y d KQ ˆ 2 2 (c) y d KQ ˆ 3 . 2 2 2 (d) y d KQ ˆ 3 . 2 2 2 (e) ' ˆ 2 2 x d KQ (f) ' ˆ 2 2 x d KQ (g) y d KQ ˆ 4 . 0 2 2 (h) none Solution: In the O'-frame both particles are at rest and the electric field at particle 2 due to particle 1 is y d KQ E at = ˆ 2 2 r and the electric force on particle 2 is thus y d KQ E Q F at on = = ˆ 2 2 2 2 r r . Part B (4 points): What is the magnetic force that the -Q particle exerts on the +Q particle in the particle frame ? ( express your answer as a vector ) Answer: zero Solution: In the O'-frame there is no magnetic force on the particles since they are at rest (and there is no magnetic field).
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2061x2_solutions_fa02 - PHY2061 R. D. Field PHY 2061 Exam 2...

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