MP_Assignment#4_soln - 3/20/11 1:36 PM Assignments Page 1...

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Unformatted text preview: 3/20/11 1:36 PM Assignments Page 1 of 26 MP_Assignment#4 Due: 8:00am on Wednesday, March 2, 2011 Note: You will receive no credit for late submissions. To learn more, read your instructor's Grading Policy Electric Field Due to Increasing Flux Description: Step by step application of Faraday's law for B increasing linearly with time. Learning Goal: To work through a straightforward application of Faraday's law to find the EMF and the electric field surrounding a region of increasing flux Faraday's law describes how electric fields and electromotive forces are generated from changing magnetic fields. This problem is a prototypical example in which an increasing magnetic flux generates a finite line integral of the electric field around a closed loop that surrounds the changing magnetic flux through a surface bounded by that loop. A cylindrical iron rod with cross-sectional area is oriented with its symmetry axis coincident with the z axis of a cylindrical coordinate system as shown. It has a uniform magnetic field inside that varies according to . In other words, the magentic field is always in the positive z direction, and it has no other components. For your convenience, we restate Faraday's law here: , where is the line integral of the electric field, and the magnetic flux is given by , where is the angle between the magnetic field and the local normal to the surface bounded by the closed loop. Direction : The line integral and surface integral reverse their signs if the reference direction of or is reversed. The right-hand rule applies here: If the thumb of your right hand is taken along , then the fingers point along . You are free to take the loop anywhere you choose, although usually it makes sense to choose it to lie along the path of the circuit you are considering. Part A Find , the electromotive force (EMF) around a loop that is at distance from the z axis, where is restricted to the region outside the iron rod as shown. Take the direction shown in the figure as positive. Hint A.1 Selecting the loop Edit Assignment Settings per Student Student View Summary View Diagnostics View Print View with Answers [ Print ] 3/20/11 1:36 PM Assignments Page 2 of 26 Since you want to find , but Faraday's law determines only an integral of the field, you must select the loop in such a way that it involves only one value of and has a constant projection of along it. This would be a circle with fixed (at any : the rod extends infinitely in the z direction). Hint A.2 Find the magnetic flux Find the magnetic flux at time . Hint A.2.1 Flux integral The flux integral for a constant field is the value of the magnetic field component perpendicular to the surface selected times the area, . The area is the region in which the field is present and also is inside the loop selected....
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MP_Assignment#4_soln - 3/20/11 1:36 PM Assignments Page 1...

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