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
2
1
Q
Q
4
1
5
15
1
4
1
1
1
>> A = [1/4 1/5 ; 1/5 1/4] ;
>> V = [1 ; 1] ;
>> Q = V’ / A % ‘transposeQ =
2.2222 2.2222
>> QQ = A \ V;
QQ = 2.2222 2.2222
or
complications???
The potential @ each charge sphere is specified as V1 or V2
Locations are with respect to an origin.
r1 r2
4
1
V
V
2
1
2
1
Q
Q
22 rr
1
12 rr
1
12 rr
1
11 rr
1
solution to singularity
a4
Q)j,j(V.e.i
Assume that the potential is uniform within the sphere and it is equal to the value at its edge r = a.
%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
> 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
%calculate matrix elements
%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);
%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)
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.