ECE 520.219-220, Fields, Matter, and Waves, Fall'09 <br> <h2> <a href=""> ECE 520.219-220, Fields, Matter, and Waves </a> </h2> <br> taught by <a href=""> Prof. Alexander Kaplan </a>, Barton Hall, #304, <br> at <a href=""> Elect. & Computer Eng. Dept.</a> of <a href=""> JHU </a> <br> <p> <br> The class is held on Mondays & Wednesdays, in Barton Hall, #117, 3:00-4:15. First meeting -- Sept. 2'09 <br> Class assistant: Beibei Zhang, Barton Hall, #404, <br> Office hours: Alex Kaplan, Mondays, 1:00--3:00 pm <br> Beibei Zhang, Wed. 12-2 <br> <br> Home work #1 <br> Problems: <br> 1.1, 1.5, 1.7, 1.9 (a,b), 1.13, 1.19, 1.25 <br> <a href="hw1.pdf"> see PDF-file with all the above problems </a> <br> <br> Home work #2 <br> Problems: <br> 2.2, 2.6, 2.8, 2.14, 2.21, 2.25 <br> plus the problem of field vs distance R from a center of sphere with the total charge Q and radius R_0. <br> <br> <a href="solut.Hw2.PDF"> see PDF-file with the solutions of all the above problems (including the one with a charged sphere) </a> <br> <br> Home work #3 <br> Problems: <br> 3.4, 3.10, 3.12, 3,14, 3.20, 4.4, 4.8, 4.12, 4,16 <br> <a href="solut.Hw3.pdf"> see PDF-file with the solutions of the above problems </a> <br> <br> Home work #4 <br> Problems: <br> 4.22, 4.28, 4.30, 5.4, 5.6, 5.10 <br> plus two other problems: <br> <br> 4.A: <br> There are two parallel strings charged with the linear charge density rho_L and -rho_L spaced by the distance d, forming a linear dipole. Find electrical field at the distance R from the center line of the system in the plane normal to the strings, in a far-field area (R >> d) <br> <br> 4.B: <br> An unmoving electron is positioned at a very large distance R away from a proton, and them set out free. Attracted by a positively charged proton, it started to move. Evaluate its velocity in terms of velocity of light in free space, when it reaches the point of 0.5 angstrem from the proton. Assume that proton has an infinite mass. <br> <br> <a href="solut.Hw4.PDF"> see PDF-file with the solutions of all the above problems (including 4.A and 4.B). </a> <br> <br> Home work #5 <br> Problems: <br> 5.12, 5.16, 5.18, 5. 20, 5.22 <br> plus two other problems: <br> <br> 5.A: <br> There is a sphere of radius R_0, filled with initially unmoving electrons in free space, such that the total charge is -Q. The sphere begins blowing apart due to mutual repulsion of electrons, resulting in a Coulomb explosion. Find out the dynamics of this explosion, i.e. how the sphere radius, R, changes in time. <br> <br> 5.B: <br> An electron is placed above the metall surface at the distance R. Find out the distribution of surface charges at the metall surface as the function of the distance r from the point of projection of the electon onto the surface. <br> <br> <a href="solut.Hw5.pdf"> see PDF-file with the solutions of the above problems </a> <br> <br> Home work #6 <br> Problems: <br> 5.24, 5.26, 6.1, 6.2, 6.6, 6.8, 6.10, 6.12 <br> plus one more problem: <br> <br> 6.A. A postive charge q is placed in free space in the middle between two ideally conducting infinite metallic surfaces spaced by the distance d. Find the field at any point in the middle between the surfaces at the distance R_0 from the charge. <br> <br> <a href="solut.Hw6.pdf"> see PDF-file with the solutions of all the above problems </a> <br> <br> Home work #7 <br> Problems: <br> 6.14, 6.16, 6.17, 6.19, 6.23, 6.24 <br> plus one more problem: <br> <br> 7.A. Find the capacitance of the planet Earth in terms of faradas. Assume the Earth an ideally conducting sphere. <br> <br> <a href="solut.Hw7.pdf"> see PDF-file with the solutions of all the above problems </a> <br> <br> Home work #8 <br> Problems: <br> 7.2, 7.3, 7.4, 7.7, 7.17, 7.28 <br> plus couple more problems: <br> <br> 8.A. Write a Laplas-like 1D-equation for the potential V, if the dielectric constant of a material is changing in the x-axis as epsilon=1+(x/a)^2, where "a" is some characteristic length. Try to solve it for the potential V. <br> <br> 8.B. Derive eqns (7.20) and (7.21) in a book; also check out the eqn preceeding (7.17). <br> <br> <a href="solut.Hw8.pdf"> see PDF-file with the solutions of all the above problems </a> <br> <br> Home work #9 <br> Problems: <br> 7.19, 7.20 <br> plus 3 more problems: <br> <br> 9.A. For the solution, eq. (7.39), considered in the book find the family of equipotential surfaces, for which only one term in (7.39) would suffice. (You may need to look carefully through the Chapter 7!) <br> <br> 9.B. Two wedges in free space (2D-case) with a common axis and each having wedge angle 2*phi, almost touch each other. Find spatial diostribution of potential (and equipotential surfaces) and field distribution in the space around them. The same question about two conuses with the same conical angle. (The same instruction as in previous problem.) <br> <br> 9.C. An infinite string with the velocity "v" of wave propagation was deformed in the beginning to form a equal-sided triangular on its shape, and then let go. What waves would propagate in it after that? find their exact solution of the problem. <br> <br> <a href="solut.Hw9.pdf"> see PDF-file with the solutions of all the above problems </a> <br> <br> Home work #10 <br> Problems: <br> 8.2, 8.4(a)(with extra, see below), 8.6, 8.10, 8.12, 8.13, 8.22 <br> plus 2 more problems: <br> <br> Extra to 8.4(a)of a book: find field H at any point in the z-axis; examine how it attunuates as |z|->infinity. <br> <br> 10.A. Prove eq (8.31) in the book by using the defenition of both NABLA operators in terms of partial derivatives. <br> <br> <a href="solut.Hw10.pdf"> see PDF-file with the solutions of all the above problems </a> <br> <br> <a href="project.topics.09.pdf"> Suggested topics for the course project/presentation </a> <br> <br> Take-Home Final Exam <br> Problems: <br> 2.22, 3.6, 4.18, 7.8, 8.5 <br> plus 2 more problems: <br> <br> F.A. Two metallic plates parallel to each other, spaced by "d" and positioned vertically, are immersed into a liquid with the dielectric constant eps_r > 1, above which there is a free air. The plates are charged oppositely, with the charge on one of them being Q. What happened with the liquid between them? Will it be pushed up or down? and how far? What happened to the liquid if instead of charging the plates with a fixed charge you connect them to a battery with a fixed voltage "V"? <br> You may use the relationship for the energy of field (4.46) or of the capacitor, (6.28). <br> <br> F.B. Two ideally conducting and parallel to each other rails are immersed in a dc magnetic field "H_0" normal to the plane of the rails. An ideally conducting wire maintain a connection between the rails, but is allowed to slide along them, while staying normal both to the rails and to the magnetic field. There is a constant current "I" flowing through one rail to the wire to the another rail. The magnetic field is turned on at the moment "0". How far would the wire move under the action of the magnetic field after time "t"? what would be its speed? Neglect the magnetic field generated by the current itself. <br> <br> <a href="solutions.FINAL.pdf"> see PDF-file with the solutions of all the final exam problems </a> <br> <br> The finals: <br> <br> <a href="FINAL.520.219.2009Fall_anonymous.pdf"> Your anonymous total grades and the finals are posted here </a> <br> <br> Your graded final exam papers can be found in a big enevelope attached to the door of my office. <br> <br> If you have any complaints, please email me and I will look into that; in the end of the week I will turn in the final grading to Registar. <br> <br> Alex Kaplan <br>