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Unformatted text preview: ECE 312 Midterm 1 Students: The Ohio State University’s Code of Student Conduct (Section 33352304) 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 zaxis. 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 Crosssection Ital ...
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 Spring '08
 Johnson,J

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