surface charge columb law

How Matlab used the columb law to calculate the electric field for points charges , surfaces

does the surface is divided into points charges? What is the approach for this fuction ?

function SurfaceChargeField

% Program to find V and E of surface (rectangular and circular)

% Charge Distribution

%=============================================

% Adjust These Parameters

% Evaluation of electric field at P(x,y,z)

PLoc=[0 0 1] ;

% The discretization element side d

ElementSize=0.001;

Eps0=10e-9/(36*pi);

Eps=Eps0; % Medium is free space

%=====================Surface Parameters

% Charge distribution is assumed to be on a rectangle, Disk or Partial Disk

SurfParam.SurfaceShape= 2; % 1 for rectangle Patch

% 2 for disk, annular disk or partial disk

SurfParam.Rho0=5*10e-9 ; % Unifrom Rho

SurfParam.UseRandChargeDist = 0; % 0 for uninform charge distribution and 1 for random distribution

if SurfParam.SurfaceShape ==1 % Rectangular Patch Shape

SurfParam.X=[0 1]; % X Min and Max

SurfParam.Y=[-1 1]; % Y Min and Max

elseif SurfParam.SurfaceShape ==2

SurfParam.DiskRad =2 ; % Outer Radius of disk

SurfParam.InnerDiskRad=1; % Inner disk rad (Use 0 for full disk)

SurfParam.Phi=[0 2*pi]; % Start and End Angles For Partial Disk

end

%============================================================

%==========================================================

% Use function rho_s_fun below to adjust the charge density

dx=ElementSize;

dy=ElementSize;

ds=dx*dy; % Square Element Areal

format short % prints only 6 decimal places

%====================Check Parameters======================

if SurfParam.SurfaceShape== 1

if (SurfParam.X(2) <=SurfParam.X(1) || SurfParam.Y(2) <=SurfParam.Y(1))

display('Error Check Dimension Values');

return;

end

elseif SurfParam.SurfaceShape== 2

if (SurfParam.DiskRad <=SurfParam.InnerDiskRad)

display('Error DiskRad is Tool Small');

return;

end

%======= Area Around the Disk

SurfParam.X=SurfParam.DiskRad*[-1 1];

SurfParam.Y=SurfParam.DiskRad*[-1 1];

end

tic;

X= SurfParam.X(1) : dx : SurfParam.X(2);

Y= SurfParam.Y(1) : dy : SurfParam.Y(2);

[XLoc,YLoc]=meshgrid(X,Y);

YLoc=flipud(YLoc); % Make First Row For Maximum Y

SurfParam.ArraySize=size(XLoc);

ZLoc=zeros(SurfParam.ArraySize);

% RVec is (r - r')

RVec=cat(3,(PLoc(1)-XLoc),(PLoc(2)-YLoc), (PLoc(3)-ZLoc)); % | r - rprime |

RMag=sqrt(RVec(:,:,1).^2+RVec(:,:,2).^2+RVec(:,:,3).^2);

rho_s=rho_s_fun(XLoc,YLoc,SurfParam);

%=========== Calculate Potential V

VNumerator=ds*rho_s;

VDenominator=4*pi*Eps*RMag;

ElemV=VNumerator./VDenominator;

VField=sum(sum(ElemV));

%=========== Calculate E Field

ENumerator=ds*repmat(rho_s,1,1,3).*RVec;

EDenominator=4*pi*Eps*repmat(RMag.^3,1,1,3); % | r - rprime | ^ 3

ElemField=ENumerator./EDenominator;

EField=[sum(sum(ElemField(:,:,1))),sum(sum(ElemField(:,:,2))),sum(sum(ElemField(:,:,3)))];

% ===============Display results

figure

imagesc(rho_s);

title('Charge Distribution');

colormap(gray)

colorbar

disp('The computed potential in V is');

disp(VField);

disp('The computed electric field in V/m is');

disp(EField);

toc

end

function rho_s=rho_s_fun(XLoc,YLoc,SurfParam)

SurfaceShape=SurfParam.SurfaceShape;

Rho0=SurfParam.Rho0;

if SurfaceShape==1

rho_s=Rho0*ones(SurfParam.ArraySize) ; % uniform charge density

%=================================================

elseif SurfaceShape==2

%For Disk set rho_s to be 0 outsie the disk area

DiskRad=SurfParam.DiskRad;

InnerDiskRad=SurfParam.InnerDiskRad;

ElementRho=sqrt(XLoc.^2+YLoc.^2);

PhiMin=SurfParam.Phi(1);

PhiMax=SurfParam.Phi(2);

ElemPhi=wrapTo2Pi(atan2(YLoc,XLoc)); % Notice atan2 function gives angle from -pi to pi

rho_s=zeros(size(XLoc));

DiskElem=(ElementRho >= InnerDiskRad & ElementRho <= DiskRad & ...

ElemPhi >= PhiMin & ElemPhi <= PhiMax);

% We choose elements inside the disk

rho_s=Rho0*DiskElem ; % Uniform Charge

%======================================================

% Example of Nonuniform charge density

% rho_s=Rho0*ElementRho.^2.*DiskElem;

%===========================================

% Rand Charge Distribution ( TO show elements)

if SurfParam.UseRandChargeDist==1

rho_s=rho_s.*randn(size(rho_s));

end

%============================

end

end