Magnetic fields 2-solutions

Magnetic fields 2-solutions - gilvin(jg47854 17 Magnetic...

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gilvin (jg47854) - 17 Magnetic fields 2 - meyers - (21235) 1 This print-out should have 15 questions. Multiple-choice questions may continue on the next column or page - find all choices before answering. This homework is due Friday, April 15, at midnight Tucson time. 001 (part 1 of 2) 10.0 points In an experiment designed to measure the strength of a uniform magnetic field produced by a set of coils, electrons are accelerated from rest through a potential difference of 227 V. The resulting electron beam travels in a circle with a radius of 12 cm. The charge on an electron is 1.60218 × 10 −19 C and its mass is 9.10939 × 10 −31 kg. Assuming the magnetic field is perpendic- ular to the beam, find the magnitude of the magnetic field. Correct answer: 0.000423386 T. Explanation: Let : e = 1.60218 × 10 −19 C , r = 12 cm = 0.12 m , V = 227 V , and m = m e = 9.10939 × 10 −31 kg . Since K i = 0 and K f = 1 2 m v 2 , we have 1 2 m v 2 = √e| V = (9.10939 × 10 31 kg) (1.60218 × 10 −19 C) × (8.93591 × 10 6 m/s) (0.12 m) = 0.000423386 T . 002 (part 2 of 2) 10.0 points What is the angular velocity of the electrons? Correct answer: 7.44659 × 10 7 rad/s. Explanation: For the angular velocity of the electron we obtain ω = v r = 8.93591 × 10 6 m/s 0.12 m = 7.44659 × 10 7 rad/s . 003 10.0 points A particle with a positive charge q and mass m is undergoing circular motion with speed v. At t = 0, the particle is moving along the negative x axis in the plane perpendicular to the magnetic field B , which points in the positive z direction as shown in the figure below. y B v = = 2 |e| V m e 2 (1.60218 × 10 −19 C) (227 V) 9.10939 × 10 −31 kg v x z = 8.93591 × 10 6 m/s . From conservation of energy, the increase in the electrons’ kinetic energy must equal the change in their potential energy |e|V : F = e v B = m v 2 r B = m v |e| r Find the period of the circular motion; i.e., the time takes for the particle to complete one revolution. 1. T = 2 π m q B correct 2. T = q B m 3. T = 2 π q B m

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4. T = 2m B q 5. T = π q B m 6. T = 2 m q B 7. T = m B q 8. T = 2 π m B gilvin (jg47854) - 17 Magnetic fields 2 - meyers - (21235) 2 Explanation: Let : I = 12 A , B = 99 mT = 0.099 T , L x = −6 m , and L z = 8.7 m . Basic Concept: Magnetic Force on a Cur- rent: F q 9. T = m q B 10. T = 2 q B m Explanation: The force on a charge q in magnetic field is = I L × B Solution: We have to add up the forces that the magnetic field produces on each segment of wire. For the segment along the z-axis: F z−seg = I L × B F B = q v × B . The centripetal force F
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Magnetic fields 2-solutions - gilvin(jg47854 17 Magnetic...

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