exam1_sol_003 - PHY2049 Fall 2008 Prof. S. Hershfield Prof....

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Unformatted text preview: PHY2049 Fall 2008 Prof. S. Hershfield Prof. Y. Takano Prof. P. Avery Sep. 24, 2008 Exam 1 Solutions Note that each problem has three versions, each with different numbers and answers (sepa- rated by |. The numbers for each question and its correct answer are listed in order for all three versions. 1. A muon (same charge as an electron but 206 times its mass) circles a beryllium nucleus (4 protons, 5 neutrons) at a distance of 0.120 | 0.216 | 0.562 picometers. What is its velocity? Answer : 6390 km/s | 4770 km/s | 2950 km/s Solution : The magnitude of the force on the muon is F = k (4 e )( e ) / r 2 = ma = mv 2 / r ). Solving for the velocity yields v = (4 ke 2 / mr ) 1/2 . 2. As shown in the figure (not drawn to scale), two charges Q 1 and Q 2 are held in place a distance L = 2 cm apart. When another charge is placed at point X, located 1.65 cm | 2.32 cm | 0.79 cm to the left of Q 1 , it is found to be in equilibrium. If Q 1 = 5 C, what is Q 2 ? Answer : 24.5 C | 17.3 C | 62.4 C Solution : Note that Q 2 must be negative to balance the force due to Q 1 at point X. Let Q 3 be the charge at X. The x-component of the force due to Q 1 is F 1 = kQ 1 Q 3 / ( x ) 2 and the x-component of the force due to Q 2 is F 2 = kQ 2 Q 3 / ( L x ) 2 . Equating these two yields Q 2 = Q 1 ( L x ) 2 / x 2 ....
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exam1_sol_003 - PHY2049 Fall 2008 Prof. S. Hershfield Prof....

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