hw10a - aldawsari(ma28683 HW10 Betancourt(16856 This...

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aldawsari (ma28683) – HW10 – Betancourt – (16856) 1 This print-out should have 12 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 27.1-27.8 001 10.0 points A charged particle is projected with its initial velocity parallel to a uniform magnetic field. What is the resulting path? 1. straight line perpendicular to the field. 2. circular arc. 3. straight line parallel to the field. correct 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 (part 1 of 3) 10.0 points The magnetic field over a certain range is given by vector B = B x ˆ ı + B y ˆ , where B x = 8 T and B y = 5 T. An electron moves into the field with a velocity vectorv = v x ˆ ı + v y ˆ + v z ˆ k , where v x = 8 m / s, v y = 3 m / s and v z = 6 m / s. The charge on the electron is 1 . 602 × 10 - 19 C. What is the ˆ ı component of the force ex- erted on the electron by the magnetic field? Correct answer: 4 . 806 × 10 - 18 N. Explanation: Let : v x = 8 m / s , v y = 3 m / s , v z = 6 m / s , q = 1 . 602 × 10 - 19 C , B x = 8 T , and B y = 5 T . The force exerted on the electron by the mag- netic field is given by vector F = qvectorv × vector B = q vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle ˆ ı ˆ ˆ k v x v y v z B x B y 0 vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle = q [ v z B y ˆ ı + v z B x ˆ + ( v x B y v y B x ) ˆ k ] = ( 1 . 602 × 10 - 19 C) {− (6 m / s) (5 T)ˆ ı + (6 m / s) (8 T)ˆ + [(8 m / s) (5 T) (3 m / s) (8 T)] ˆ k } = (4 . 806 × 10 - 18 N)ˆ ı + ( 7 . 6896 × 10 - 18 N)ˆ + ( 2 . 5632 × 10 - 18 N) ˆ k 003 (part 2 of 3) 10.0 points
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