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PHY303L HW8

# PHY303L HW8 - thwing(jrt2329 Homework 08 Yao(59110 This...

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thwing (jrt2329) – Homework 08 – Yao – (59110) 1 This print-out should have 25 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points A charged particle is projected with its initial velocity parallel to a uniform magnetic field. What is the resulting path? 1. circular arc. 2. straight line parallel to the field. correct 3. straight line perpendicular to the field. 4. spiral. 5. parabolic arc. Explanation: The force on a moving charge due to a magnetic field is given by vector F = qvectorv × vector B . If vectorv and vector B are parallel, then vectorv × vector B = 0 . Hence the force on the particle is zero, and the particle continues to move in a straight line parallel to the field. 002 10.0 points A static uniform magnetic field is directed into the page. A charged particle moves in the plane of the page following a counter- clockwise spiral of increasing radius as shown. B B Neglect the effect due to gravity. What is a reasonable explanation? 1. The charge is negative and slowing down. 2. The charge is positive and slowing down. 3. The charge is positive and with a constant speed. 4. The charge is neutral and slowing down. 5. The charge is positive and speeding up. correct 6. None of these 7. The charge is negative and speeding up. 8. The charge is neutral and speeding up. 9. The charge is negative and with a con- stant speed. 10. The charge is neutral and with a constant speed. Explanation: We know that when a charged particle moves in a uniform magnetic field with a constant speed, it undergoes a circular mo- tion with the centripetal force provided by the magnetic force, namely m v 2 r = q v B , so we know that the radius is in fact propor- tional to the speed, r = m q B v . Since the particle follows a spiral of increasing radius, we can judge that it is speeding up. The magnetic force vector F = qvectorv × vector B must be in the direction for the centripetal force ˆ r (pointed inward) of this particle in counter- clockwise circular motion. Since vectorv × vector B is in the negative ˆ r direction, the particle has a positive charge.

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thwing (jrt2329) – Homework 08 – Yao – (59110) 2 003 10.0 points Hint: Use non-relativistic mechanics to work this problem. A cyclotron is designed to accelerate pro- tons to energies of 3 . 6 MeV using a magnetic field of 0 . 5 T. The charge on the proton is 1 . 60218 × 10 19 C and its mass is 1 . 67262 × 10 27 kg. What is the required radius of the cy- clotron? Correct answer: 0 . 548297 m. Explanation: Let : B = 0 . 5 T , q = 1 . 60218 × 10 19 C , E = 3 . 6 MeV = (3 . 6 × 10 6 eV) × (1 . 602 × 10 19 J / eV) , = 5 . 7672 × 10 13 J , and m = 1 . 67262 × 10 27 kg . The speed of the proton is v = radicalbigg 2 E m = radicalBigg 2 (5 . 7672 × 10 13 J) (1 . 67262 × 10 27 kg) = 2 . 62602 × 10 7 m / s , where E is the kinetic energy of the proton.
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PHY303L HW8 - thwing(jrt2329 Homework 08 Yao(59110 This...

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