24-1 - brown (twb493) – ch24-h1 – chiu – (56565) This...

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Unformatted text preview: brown (twb493) – ch24-h1 – chiu – (56565) This print-out should have 15 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 1 002 (part 2 of 3) 10.0 points Which of the following arrows best indicates the direction of the magnetic field at the ×? 001 (part 1 of 3) 10.0 points N closely spaced turns of wire are wound in the direction indicated on a hollow, plastic ring of radius R, with circular cross section, as in the figure below. VIII I VII II III VI IV V R 1. II 2. IV 3. III I I If the current in the wire is I , determine the magnetic field B at the location indicated by the ×, at the center of the cross section of the ring. µ0 2 N I correct 1. B = 4π R µ0 N I 2. B = π R2 µ0 N I 3. B = 4π R µ0 N I 4. B = πR µ0 2 N I 5. B = 4π R 2 Explanation: Use Ampere’s Law with a circular loop C of radius R along the toroid’s midline. B · d = µ0 I C 2 π R B = µ0 N I ⇒B= µ0 2 N I . 4π R 4. V 5. VII 6. VIII correct 7. VI 8. I Explanation: Knowing which way the current is moving through the wire, we can use the right hand rule to determine that the magnetic field is going clockwise through the cross section of the ring, meaning that at the × it is directed toward the upper-left, or arrow VIII. 003 (part 3 of 3) 10.0 points Throughout this region there is a uniform electric field E into the paper. This electric field begins to increase at a rate dE/dt, and there continues to be a current I in the wire. Now what is the magnitude of the magnetic field at the indicated point? 1. B = µ0 2 N I R dE + 2 4π R 2 π c2 dt brown (twb493) – ch24-h1 – chiu – (56565) 2. B = µ0 N I R 2 dE +2 πR 4 c dt 3. B = µ0 N I R dE +2 4π R 2 c dt 4. B = R dE µ0 2 N I +2 correct 4π R 2 c dt 5. B = µ0 2 N I R 2 dE + 4π R 2 π c2 dt Explanation: Use Ampere’s law, as modified by Maxwell, around the same loop C : B · d = µ0 I + µ0 0 C 2 π R B = µ0 I + µ0 ⇒B= d ΦE dt 0A dE dt µ0 0 π R 2 d E µ0 2 N I + 4π R 2πR dt = µ0 2 N I R dE +2 4π R 2 c dt 004 10.0 points If the magnetic field in a particular pulse has a magnitude of 3.5 × 10−5 T (comparable to the Earth’s magnetic field), what is the magnitude of the associated electric field? Remember that c = 3 × 108 m/s. Correct answer: 10500 N/C. Explanation: Knowing that 005 (part 1 of 3) 10.0 points In the figure below, electromagnetic radiation is moving to the right, and at this time and place the electric field is horizontal and points out of the page. The magnitude of the electric field is E = 2550 N/C. The speed of light is c = 3 × 108 m/s. Take +x to be toward the right, +y to be upward, and +z to be out of the page toward you. Direction of propagation E = 2550 N/C What is the associated magnetic field at this time and place? Begin by finding the x component, Bx . Correct answer: 0 T. Explanation: We can determine the nonzero component of B by using the right-hand rule. With the wave propagating in the +x direction, and the electric field in the +z direction, the magnetic field must point in the −y direction. Therefore the x and z components of the magnetic field are both zero. 006 (part 2 of 3) 10.0 points Find By . Correct answer: −8.5 × 10−6 T. Explanation: We know that the magnetic field points along the −y axis, so we just need to find the magnitude, which we can do using E E c= 2 , . c= B B we can write E E =c B = (3 × 108 m/s)(3.5 × 10−5 T) = 10500 N/C . B= c 2550 N/C = 3 × 108 m/s = 8.5 × 10−6 T . brown (twb493) – ch24-h1 – chiu – (56565) So the y component is −8.5 × 10−6 T . Correct answer: 0 T. Explanation: See the explanation for part 1. 1. 0, 0, −1 correct 008 (part 1 of 2) 10.0 points At a time t0 , an electric field is detected in the region shown on the left diagram in the figure below. The electric field is zero at all other locations. At a later time t1 , an electric field is detected in the region shown on the right diagram. The electric field is still zero elsewhere. You conclude that an electromagnetic wave is passing through the region. The +z direction points out of the page (toward you). t0 y x netic wave is propagating in the −y direction. 009 (part 2 of 2) 10.0 points If you were to measure the magnetic field in the region where the electric field is nonzero, what would be the direction of the magnetic field? 007 (part 3 of 3) 10.0 points Find Bz . y 3 t1 x What is the direction of propagation of the electromagnetic wave? Choose the unit vector corresponding to this direction. 2. 1, 0, 0 3. 0, 0, 1 4. 0, 1, 0 5. 0, −1, 0 6. −1, 0, 0 Explanation: We know that E × B points in the direction of propagation. Pointing your thumb along the −y axis to indicate the direction of propagation and pointing your fingers along the −x direction to indicate the direction of the electric field, the right-hand rule indicates that the magnetic field must point along the −z axis. 010 (part 1 of 2) 10.0 points A pulse of electromagnetic radiation is propagating in the +y direction. You have two devices that can detect electric and magnetic fields. You place detector 1 at location 1. 0, 1, 0 2. 0, 0, −1 0, −8, 0 m and detector 2 at location 0 , 8 , 0 m. 3. 0, 0, 1 4. −1, 0, 0 5. 1, 0, 0 6. 0, −1, 0 correct Explanation: Based on the change in location of the electric field between t0 and t1 , the electromag- At time t = 0, detector 1 detects an electric field in the −x direction. At that instant, what is the direction of the magnetic field at the location of detector 1? Choose the unit vector corresponding to this direction. 1. 0, 0, 1 correct 2. 0, 1, 0 brown (twb493) – ch24-h1 – chiu – (56565) The key to this problem is to begin by deciding the direction of the magnetic field. Since the wave is propagating in the −z direction, and the electric field is in the +x direction, the magnetic field must be in the −y direction, according to the right-hand rule. This means the x component of the magnetic field is zero. 3. 0, 0, −1 4. 0, −1, 0 5. 1, 0, 0 6. −1, 0, 0 Explanation: The direction of propagation is in the direction of E × B , which is in the +y direction. Using the right-hand rule, B must be in the +z direction. 011 (part 2 of 2) 10.0 points At what time will detector 2 detect electric and magnetic fields? Remember that c = 3 × 108 m/s. Correct answer: 5.33333 × 10−8 s. 013 (part 2 of 3) 10.0 points What is By ? Correct answer: −0.0253333 T. Explanation: Since we know the magnetic field points along the −y direction, we know this component is nonzero and we know the sign. We just need the magnitude, which we can find using E Explanation: The wave propagates at the speed of light. So we can write distance c= ∆t distance ⇒ ∆t = c 16 m 8 m − (−8 m) = = 8 m/ s 3 × 10 3 × 108 m/s = 5.33333 × 10−8 s . 012 (part 1 of 3) 10.0 points A pulse of radiation propagates with velocity 0, 0, −c m/s where c = 3 × 108 m/s. The electric field in the pulse is 7.6 × 106 N/C, 0, 0 N/C. What is the magnetic field in the pulse? First give the x component, Bx . Correct answer: 0 T. Explanation: 4 c= . B We have E B= c 7.6 × 106 N/C = 3 × 108 m/s = 0.0253333 T . Taking the sign into account, the y component is −0.0253333 T . 014 (part 3 of 3) 10.0 points What is Bz ? Correct answer: 0 T. Explanation: Following the explanation for part 1, the z component of the magnetic field is zero. 015 10.0 points Consider the electromagnetic wave pattern as shown in the figure below. brown (twb493) – ch24-h1 – chiu – (56565) E B What is the direction in which the wave is traveling? 1. from-right-to-left. 2. undetermined, since the figure shows a standing wave. 3. from-left-to-right. correct Explanation: The direction of traveling is the direction of E × B ; i.e., from-left-to-right. 5 ...
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This note was uploaded on 12/01/2011 for the course PHY 303L taught by Professor Turner during the Fall '08 term at University of Texas at Austin.

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