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ECE312_W09_Exam1_Solutions

ECE312_W09_Exam1_Solutions - ECE 312 Midterm 1 Students The...

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Unformatted text preview: ECE 312 Midterm 1 Students: The Ohio State University’s Code of Student Conduct (Section 3335-23-04) defines academic misconduct as: “Any activity that tends to compromise the academic integrity of the University, or subvert the educational process.” Examples of academic misconduct include (but are not limited to) plagiarism, collusion (unauthorized collaboration), copying the work of another student, and possession of unauthorized materials during an examination. Ignorance of the University’s Code of Student Conduct is never considered an "excuse” for academic misconduct. If I suspect that a student has committed academic misconduct in this course, I am obligated by University Rules to report my suspicions to the Committee on Academic Misconduct. If COAM determines that you have violated the University’s Code of Student Conduct (i.e., committed academic misconduct), the sanctions for the misconduct could include a failing grade in this course and suspension or dismissal from the University. Professor Reano EE Honor Code Pledge: "No aid given, received, or observed" Signature: Samaria S’ 94% Print name here: Problem 1. (25 points) Consider a capacitor consisting of two parallel conducting plates separated by a distance d. The space between the plates contains two adjacent dielectrics, one with permittivity 81 and surface area A1 and another with 82 and A2. The surface areas are large so that one can neglect fringing at the edges. Capacitor with parallel dielectric section Equivalent circuit a) (10 points) Calculate the stored energy in each section and use the result to calculate C1 in terms of 81, A1, and d, and C2 in terms of 82, A2, and d. We. = £00” 316415“ = 1(a). v2 , A 2 q, 1 . '1 2. W61 2 JCZV : 1ez(y)4bt{;1 £241 v z 2’ Z 4‘! 5 7 b) (15 points) Use the total energy stored in the capacitor to calculate the overall capacitance C for the whole structure. Problem 2. (25 points) A planar circular loop of current of radius a centered on the origin and oriented with surface normal in the 2 direction carries a current I in the ¢ direction. a) (20 points) Find the 17 field along the z-axis. Show all details for full credit. Score = 0 for only listing final result. L b) (5 points) At 2 = 0, show that |H| = Problem 3. (25 points) An infinitely long wire carrying a 25 A current (11) in the positive x direction is placed along the x—axis in the vicinity of a 20 turn circular loop located in the xy plane as shown. The magnetic field at the center of the loop is zero. ® ’I a) (10 points) What is the direction of the current flowing in the loop? ‘ Mum ga ! (I = 2m .l' b) (15 points) What is the magnitude of the current flowing in the loop in Amps? Show all details for full credit. Score = 0 for only listing final result. _ .— A Wine: H=%_IJ_ 2rd ._.. A _ Lap—r: H = '%;L_L.M a M, 0| Problem 4. (25 points) A thin current element extending between 2 = -L/2 and z = +L/2 carries a current I along + 2 through a circular cross section of radius a. Find the vector magnetic potential A at a point P located very far from the origin (assume R is so much larger than L that point P may be considered to be at approximately the same distance from every point along the current element). ’7. _, 370W U2 {hr E“ 450 Cross-section Ital ...
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