hw10sols - COLORADO STATE UNIVERSITY DEPARTMENT OF PHYSICS...

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Unformatted text preview: COLORADO STATE UNIVERSITY DEPARTMENT OF PHYSICS Spring Semester 2008 Ph142 - Physics for Scientists and Engineers PROBLEM SET 10 - CHAPTER 28 - MAGNETIC INDUCTION - PART II DUE AT THE START OF RECITATION CLASS ON 10 APRIL 2008 Some guidelines for problem solving (whether handed in and graded or not): Focus is on understanding and implementation, not “plug and chug" problems. Almost every problem will involve some level of conceptual understanding and some challenge in the mathematical set-up and parameterization. Required format: (1) Do your work on grid style engineering paper. (2) Use one side of the page only. ('3) Start each problem on a new page and state the problem number clearly. (4) Put your name, section number, problem set number, and due date on every page. ('5) include proper and reasonably professional looking diagrams or sketches for each problem. (6) Assemble in problem order (#1. #2, #3, etc.) and staple your pages in the upper left corner. Note #1: For assigned problems, your work (here and on future problem sets) should be accompanied by: (a) A clear problem statement in words, diagrams, and equations (not a regurgitation of the problem text in Tipler and Mosca, necessarily, but adequate for some one to know what the problem is without going back to the book). (b) Good clear well labeled diagrams. (c) Well developed equations with all parameters defined. (d) Graphs with clearly defined and labeled axes, etc. Note #2: You should parameterize all problems. That is, assign algebraic parameters to all relevant variables and constants, set the problem up algebraically. and solve algebraically. Only then (if numerical evaluations are rec uired), shoald you begin to plug in numbers. When you do plug in numbers, if it is a simple exercise, do as much of the evaluation as you can by hand (not by calculator). Multiply and cancel simple factors, add and subtract powers of ten, etc., to obtan a simplified numerical expression for evaluation. Often, you will find that you do not even need to do a calculator evaluation! If it is a complicated evaluation, you may wish to use some appropriate software, such as MathCad, etc. Note #4: A Problem Set will generally have from five to ten problems. if your recitation instructor decides to grade problems in some fashion, he or she may give partial credit, when deserved. However, there will be no credit for nonsense. Everything you say must make sense. Take care to do some intelligent work on ALL the problems. One completely missing problem can have a serious effect on your understanding and (if graded) on your Problem Set grade. Note #5. Don’t skimp on pages. Start each problem on a new page. Note #6. Start on a given problem set AS SOON AS IT iS MADE AVAILABLE. Work AT your solutions every day. Develop your solutions. Only when you are done, should you “write up” your solution set. When you do write it up, do so with understanding. Do not simply copy from your scratch notes. if you simply copy, without understanding, your graphs will not make sense, your equations will not make sense, and probably nothing will make sense. L3.) The problems (a) Show that L/R has units ofseconds. Hint: Use the voltage relations VR = [R and V), = Ld] fdt. (b) Show that so has units of capacitance per unit length. (c) Show that no has units of inductance per unit length. Tipler and Mosca, Problem 28—12. (a) Another variation on Tipler and Mosca, Problem 28-28. Use parameters only. Calculate the mutual inductance M of the wire-loop system by calculating gimp due a current 1 wire in the long wire. (b) Let the long wire be driven by a low frequency voltage source V(t) = V0 sin wt in series with a resistor R . (i) - Why is it prudent to have the series resistor in the circuit? (ii) Split the loop so that one can take off the induced voltage for some useful purpose. Calculate the induced voltage. (iii) What happens if one increases the number of turns on the loop winding? Ignore back emf effects. (a) As a check on your ability to "drive the bus" and your understanding of the inductance concept, sketch a long solenoid cross section on your paper. Without looking at your notes or text, apply Ampere‘s Law to obtain the magnetic field B inside the solenoid, the total flux, and the inductance L . (b) Make another sketch with more sparsely spaced windings and label current arrows that track the current around and around the windings from one end to the other. Now sketch in the electric field vectors for the back emf that is produced if you were to try to increase the current. What is the sign of this voltage relative to the initial current flow direction? Explain why you must now apply a positive voltage equal to Ld] / dt to make the current increase at the rate all/alt. Variation on Tipler and Mosca, Problem 28-49. As posed, this scheme describes a Way to make a "zero inductance" wirewound resistor by doubling back the winding. However, the inductance is not exactly zero. The parallel wires that make up the winding have a nonzero radius (taken as R for this problem) and a center to center distance of ER . (a) Make a good sketch of the double winding cross section (not the solenoid) and write dowr the magnetic field B as a function of distance (r ) from one wire center line to the other. (b) By way of approximation, assume that the residual inductance is clue to the flux between the wire centcrlines for one pair. Ignore the residual trapped flux outside of this region. Calculate this trapped flux. Show that the corresponding inductance of the total winding is given by L =(y(..(’a/4R)(l+ln 2), where t‘ is the length of the wirewound resistor, a is the radius (as in the text), and R is the radius of the wire. Tipler and Mosca, Problem 28-50. Hint: This isjust a standard solenoid, except that the parameters are now the radius (a) and length ( E ) of the wire that makes up the winding. Yourjob is one of geometry, to figure out the length ofthe solenoid and the turns from a and f. . Variation on 'l‘ipler and Mosca, Problem 28-61. Use parameters only. (i) Write the Kirchoff loop equation for the circuit for t 2 0 . i6608l’10w/ 41’1qu Lm .S‘eczwvéf. VR 3 IR VL: L [L E]=[l a] d 92:]: ER] £23 Sea cm Cb) slqm/ +5” 80 In Al: 4+ :— SEC J— U’Vllf as: cqpqct'f‘fln/Ce p94” UNIT \ijfla C ; EFL :: {TV} d 5d] 50 {50] : (C) L :: jute MIR} [L] 2 Dub] 31 ME“? = [/43 M (m Du] '3 {Li/{m r 2. Twat“? zgfllz’ ‘cvsiflx 6) J [[UX W b lm/¢~{f-«=7’: X‘ No $10K Oman/54?. 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hw10sols - COLORADO STATE UNIVERSITY DEPARTMENT OF PHYSICS...

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