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Unformatted text preview: PHY2061 R. D. Field Exam 2 Solutions Page 1 of 10 March 28, 2002 PHY 2061 Exam 2 Solutions Problem 1 (10 points): Circle true or false for following (1 point each). (a) (True or False) The speed of light in a vacuum is independent of the velocity of the source of the light and independent of the velocity of the observer. (b) (True or False) The magnetic force cannot change the speed of a charged particle. (c) (True or False) The magnetic force on a charged particle is perpendicular to the direction of the magnetic field. (d) (True or False) The electric charge of a particle depends on its velocity. (e) (True or False) The electric field produced by a charged particle depends on its velocity. (f) (True or False) It is possible to have a nonzero net magnetic force acting on an electrically neutral object. (g) (True or False) There are two ways to produce an electric field (charged particles or magnetic fields that changes with time), but only one way to produce a magnetic field (moving charges). (h) (True or False) The vector function z z y y x x z y x B & & & ) , , ( + + = r represents a possible magnetic field with magnitude given by 2 2 2 ) , ( z y x y x B + + = . Note that 3 ≠ = ⋅ ∇ B r r and hence this vector function cannot represent a magnetic field since all magnetic fields have = ⋅ ∇ B r r . (i) (True or False) The total net magnetic flux through any closed surface is always zero. (j) (True or False) Light has no mass but has energy and momentum. PHY2061 R. D. Field Exam 2 Solutions Page 2 of 10 March 28, 2002 Problem 2 (relativity, 15 points): Protons leave a particle accelerator with a speed of v = 0.8c to enter and travel through an evacuated tube that is at rest in the laboratory and is 1.0 m long, as measured by an observer in the laboratory, and then finally reach a detector. (Note: c = 3.0x10 8 m/s) Part A (3 points): How long does it take for a proton to travel from one end of the tube to the other ( in nanoseconds ) according to an observer in the laboratory frame? Answer: 4.2 Solution: In any frame distance equals speed times time and hence ns s s m m v d t 2 . 4 10 17 . 4 ) / 10 3 ( 8 . 1 9 8 = × = × = = − . Part B (4 points): How long does it take for a proton to travel from one end of the tube to the other ( in nanoseconds ) according to an observer traveling with a proton? Answer: 2.5 Solution: The proton frame is the proper time and hence ns ns t t 5 . 2 67 . 1 17 . 4 = = = = ′ γ τ , where I used 67 . 1 1 / 1 2 = − = β γ . Part C (4 points): What is the tube&s length ( in m ) as measured by an observer traveling with a proton? Answer: 0.6 Solution: In any frame distance equals speed times time and hence m m d vt v d 6 ....
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 Spring '08
 FRY
 Physics, Light, Magnetic Field, R. D., R. D. Field

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