1 / 38

method of moments

method of moments. This technique was developed in a Ph.D. thesis by Ken Mei in 1962. His adviser was Jean van Bladel. Method of moments. a known charge causes a potential what is the potential? a measured or known potential is caused by an unknown charge what was that charge?

haig
Download Presentation

method of moments

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. method of moments

  2. This technique was developed in a Ph.D. thesis by Ken Mei in 1962. His adviser was Jean van Bladel.

  3. Method of moments • a known charge causes a potential • what is the potential? • a measured or known potential is caused by an unknown charge • what was that charge? • used in em to find current distributions on antennas, scattering objects such as cubes, sleds, planes, and missles • PhD theses, faculty publications

  4. V(a) V(b) Q2 Q1 2 equations 2 unknowns

  5. V(a) V(b) Q2 Q1

  6. MATLAB!!

  7. >> A = [1/4 1/5 ; 1/5 1/4] ; >> V = [1 ; 1] ; >> Q = V’ / A % ‘transpose Q = 2.2222 2.2222 >> QQ = A \ V; or QQ = 2.2222 2.2222

  8. complications??? r1 r2 • The potential @ each charge sphere is specified as V1 or V2 • Locations are with respect to an origin.

  9. solution to singularity Assume that the potential is uniform within the sphere and it is equal to the value at its edge r = a.

  10. a = 1

  11. 1 1 1 1 1 1

  12. Q = • 4.69 2.56 4.69 -4.69 -2.56 -4.69 • >>

  13. equal charge

  14. Capacitor C = Q / V rj ri

  15. MATLAB • clear; clf; • N=9; • az=37.5; • el=5;

  16. %identify subareas • for m = 1:2 • for h = 1:N • for k = 1:N • a((m - 1)*N*N + (h - 1)*N + k, :)=[m, h, k]; • end • end • end

  17. %calculate matrix elements • for h=1:2*N*N • for k=1:2*N*N • aa=norm(a(h, :) - a(k, :)); • if aa==0 • b(h, k) = 2 * sqrt(pi); • else • b(h, k) =1 / aa; • end • end • end

  18. %set voltages on plates • for h=1:N*N • V(h) = +1/2; • V(h+N*N) = -1/2; • end

  19. %calculate charges • Q = V*inv(b); • %top plate • QA(1:N*N) = Q(1:N*N); • %bottom plate • QB(1:N*N)=Q(N*N+1:2*N*N);

  20. %plot • [x,y]=meshgrid(1:N); • for i=1:N • za(1:N,i)=QA((i-1)*N+1:(i-1)*N+N)'; • zb(1:N,i)=QB((i-1)*N+1:(i-1)*N+N)'; • end • mesh(x,y,za) • hold on • mesh(x,y,zb)

  21. QT=0; for j=1:N*N QT=QT+Q(j); end QT

  22. What have you done? You have learned a technique, to accurately calculate the capacitance of a parallel plate capacitor! Big deal!

  23. capacitance of a unit cube

  24. capacitance of a unit cube

  25. capacitance of a unit cube

  26. 2a C a

  27. note the charge density at the corner

  28. a

  29. Target shooting in Alaska

  30. 65 N; 25 E Suomi Finland

  31. Helsinki

  32. Turku

  33. Academic Kiuas-Seura is a sauna and sausage society, formed mainly by older members of Liisankadun Osakunnat, whose main task is taking sauna baths, sloping of time together and sensory testing of the sausages. The assembling is 6:30 on Tuesdays, the sausage tests continue in spite of the environmental terrorists.

More Related