method of moments

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

5

Q

4

Q

4

1aV 21

Q1Q2

V(a) V(b)

4

Q

5

Q

4

1bV 21

?Q?Q 21

Q1Q2

V(a) V(b)

2

1

Q

Q

4

1

5

15

1

4

1

4

1

)b(V

)a(V

5

Q

4

Q

4

1aV 21

4

Q

5

Q

4

1bV 21

4

1)b(V)a(Vlet

2

1

Q

Q

4

1

5

15

1

4

1

1

1

2

1

Q

Q

4

1

5

15

1

4

1

4

1

)b(V

)a(V

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.

4π

1

5

5

5

5

5

5

6

5

4

3

2

1

Q

Q

Q

Q

Q

Q1 29

141

12

14

15

1

1

1

1

1

1

4

QV

r

> Q =

> 4.69 2.56 4.69 -4.69 -2.56 -4.69

> >>

a24

s

a

0

2

0

s

r

rdrd

4

1)j,j(V

Aa s2

s

A

a

A24

s

Capacitor C = Q / V

ri

rj

> clear; clf;> N=9;> az=37.5;> el=5;

MATLAB

%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

%set voltages on plates

> for h=1:N*N> V(h) = +1/2;> V(h+N*N) = -1/2;> end

%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)

QT=0; for j=1:N*N QT=QT+Q(j);endQT

1N*1N

QT

117*117

3696.28

11.0

V6

QC sideone

sideoneC6C

V

QC

aπε4QQ

C

aπε4C

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

2a

a

C

a

42.5a

C

52.6a

C

28.7a

C

90.7a

C

Target shooting in Alaska

Suomi Finland

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.