Homework 8-solutions

Homework 8-solutions - gonzales(pag757 Homework 8...

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gonzales (pag757) – Homework 8 – Hofmann – (56745) 1 This print-out should have 10 questions. Multiple-choice questions may continue on the next column or page – Fnd all choices be±ore answering. 001 10.0 points A particle with charge q and mass m is un- dergoing circular motion with speed v . At t = 0, the particle is moving along the nega- tive x axis in the plane perpendicular to the magnetic Feld V B , which points in the positive z direction in the Fgure below. x y z Vv V B ²ind the direction o± the instantaneous ac- celeration h a at t = 0 i± q is negative. 1. h a = ˆ k + ˆ i 2. h a = ˆ i 3. h a = ˆ j correct 4. h a = ˆ i + ˆ j 5. h a = ˆ k + ˆ i 6. h a = ˆ i 7. h a = ˆ k 8. h a = ˆ j + ˆ k 9. h a = ˆ j 10. h a = ˆ k Explanation: The particle is moving along the negative x -axis in this instant = v ˆ i ; since it is moving in a circle, we need to talk about instantaneous direction. The ±orce F B is equal to q Vv × V B at all times. We know that V B is pointing in the z direction, so V B = B ˆ k , and there±ore V F B = q v ( ˆ i ) × B ˆ k = q v B ( ˆ i × ˆ k ) = q v B ˆ j . The charge q is negative ( q = −| q | ) , so V F B = −| q | v B ˆ j = | q | v B ( ˆ j ) . All quantities are positive, so the actual di- rection in which V F B points is the negative y direction, or h a = ˆ j . 002 10.0 points A particle with charge q and mass m is un- dergoing circular motion with speed v . At t = 0, the particle is moving along the nega- tive x axis in the plane perpendicular to the magnetic Feld V B , which points in the positive z direction in the Fgure below. x y z V B ²ind the period T o± oscillation; i.e. , the time it takes ±or the particle to complete one revolution. 1. T = 2 π m q B correct 2. T = 2 π q B m 3. T = 2 π m B q 4. T = m B q 5. T = q B m 6. T = m q B
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gonzales (pag757) – Homework 8 – Hofmann – (56745) 2 Explanation: Basic Concepts: Newton’s 2nd Law: F = m a . Centripetal acceleration: F c = m v 2 r . Force on charge q in magnetic ±eld (no electric ±eld): V F B = qVv × V B . Solution: The centripetal ²orce F c is pro- vided by F B , so m v 2 r = q v B v r = q B m . The period o² oscillation is T = 2 π r v , which is intuitive since the particle traverses a distance 2 π r in a revolution and, moving at speed v , takes the time T to do so. We know the ratio v r , so T = 2 π r v = 2 π m q B . 003 10.0 points On the right side o² the = sign ²or the choices, there should be the ²actor qvB. O² course the direction is just the combination o² unit vectors in the parentheses: (X +/- Y) A positively charged particle moving at 45 angles to both the y -axis and z -axis enters a magnetic ±eld (pointing out o² o² the page), as shown in the ±gure below. y z v x V B V B + q Figure: ˆ ı is in the x -direction, ˆ is in the y -direction, and ˆ k is in the z -direction. What is the initial direction o² de³ection?
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Homework 8-solutions - gonzales(pag757 Homework 8...

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