Calculate the magnetic field of square and circle loop

Contents

• calculate R-vector from the loop(X-Y plane)to Y-Z plane.

%Calculation of Square loop Magnetic Field ..

% close all windows:
clc;
clear all;
close all;

%Square loop is in the X-Y plane
% every point in the Y-Z plane(X=0)
% Magnetic Field is Evaluated

Nz=51;  % No. of grids in Z-axis
Ny=51;  % No. of grids in Y-axis
S=12;   % Length of the Square Loop
N=(S+1)*4;   % No of grids in the loop ( X-Y plane)
N4=N/4;
a=S/2;
I=3;    % current in the loop
u0=1;   % for simplicity, u0 is taken as 1 (permitivity)


% input for x plane
Xc(1:N4)=-a:1:a;
Xc(N4+1:2*N4)=a;
Xc(2*N4+1:3*N4)=a:-1:-a;
Xc(3*N4+1:N)=-a;

% input for y plane
Yc(1:13)=-a;
Yc(14:26)=-a:1:a;
Yc(27:39)=a;
Yc(40:52)=a:-1:-a;

% input for z plane

yp(1:51)=-25:1:25; % Y-coordinates of the plane where we are interested
zp(1:51)=0:1:50;% Z-coordinates of the plane where we are interested

% input for y-z coordinates
Y(1:Ny,1:Nz)=0; % This array is for 1-d to 2-d conversion of coordinates
Z(1:Ny,1:Nz)=0;

for i=1:Ny
    Y(i,:)=yp(i); % all y-coordinates value in 2-d form
end
for i=1:Nz
    Z(:,i)=zp(i);% all z-coordinates value in 2-d form
end

calculate R-vector from the loop(X-Y plane)to Y-Z plane.

%1. find the magnetic field and also the dl-vector along the current loop
%  R is the position vector pointing from loop (X-Y plane) to the
% magnetic field in Y-Z plane
% dl is the current element vector which will make up the square loop

for A=1:Ny  % for all points in the Y-Z plane, find the magnetic field
for B=1:Nz  % from the loop situated in the X-Y plane

for i=1:N-1
Rx(i)=-0.5*(Xc(i)+Xc(i+1));
Ry(i)=(Y(A,B)-(0.5*(Yc(i)+Yc(i+1))));
Rz(i)=Z(A,B);
dlx(i)=Xc(i+1)-Xc(i);
dly(i)=Yc(i+1)-Yc(i);
end
Rx(N)=-0.5*(Xc(N)+Xc(1));
Ry(N)=(Y(A,B)-(0.5*(Yc(N)+Yc(1))));
Rz(N)=Z(A,B);
dlx(N)=-Xc(N)+Xc(1);
dly(N)=-Yc(N)+Yc(1);


% calculate dl cross R is the curl of vector dl and R
for i=1:N
Xcross(i)=dly(i).*Rz(i);
Ycross(i)=-dlx(i).*Rz(i);
Zcross(i)=(dlx(i).*Ry(i))-(dly(i).*Rx(i));
R(i)=sqrt(Rx(i).^2+Ry(i).^2+Rz(i).^2);
end

%The biot savarts law equation.
Bx1=(I*u0./(4*pi*(R.^3))).*Xcross;
By1=(I*u0./(4*pi*(R.^3))).*Ycross;
Bz1=(I*u0./(4*pi*(R.^3))).*Zcross;

% Initialize sum magnetic field to be zero first
BX(A,B)=0;
BY(A,B)=0;
BZ(A,B)=0;

% create a loop by adding all magnetic field from different current elements

for i=1:N   % loop over all current elements along loop
    BX(A,B)=BX(A,B)+Bx1(i); %BX is a null field
    BY(A,B)=BY(A,B)+By1(i);
    BZ(A,B)=BZ(A,B)+Bz1(i);
end


end
end

figure(1);
plot(Xc,Yc,'linewidth',3);
axis([-20 20 -20 20]);
xlabel('X-axis','fontsize',14);
ylabel('Y-axis','fontsize',14);
title('square loop co-ordinates','fontsize',14);
h=gca;
get(h,'FontSize');
set(h,'FontSize',14);
h = get(gca, 'ylabel');
fh = figure(1);
set(fh, 'color', 'white');
grid on;

figure(2);
lim1=min(min(BZ));
lim2=max(max(BZ));
steps=(lim2-lim1)/100;
contour(zp,yp,BZ,lim1:steps:lim2);
axis([1 50 -25 25]);
xlabel('Z-axis','fontsize',14);
ylabel('Y-axis','fontsize',14);
title('BZ component','fontsize',14);
colorbar('location','eastoutside','fontsize',14);
h=gca;
get(h,'FontSize');
set(h,'FontSize',14);
h = get(gca, 'ylabel');
fh = figure(2);
set(fh, 'color', 'white');


figure(3);
lim1=min(min(BY));
lim2=max(max(BY));
steps=(lim2-lim1)/100;
contour(zp,yp,BY,lim1:steps:lim2)
axis([1 50 -25 25])
xlabel('Z-axis','fontsize',14)
ylabel('Y-axis','fontsize',14)
title('BY component','fontsize',14)
colorbar('location','eastoutside','fontsize',14);
h=gca;
get(h,'FontSize')
set(h,'FontSize',14)
h = get(gca, 'ylabel');
fh = figure(3);
set(fh, 'color', 'white');


figure(4);
quiver(zp,yp,BZ,BY,2);
axis([1 50 -25 25]);
xlabel('Z-axis','fontsize',14)
ylabel('Y-axis','fontsize',14)
title('B-field Vector flow','fontsize',14)
h=gca;
get(h,'FontSize')
set(h,'FontSize',14)
h = get(gca, 'ylabel');
fh = figure(4);
set(fh, 'color', 'white');


%%Simulation of Cicular Coil Magnetic Field

%Coil is in the X-Y plane and every point in the Y-Z plane(X=0)
%calculate Magnetic Field

Nz=51;  % No. of grids in Z-axis
Ny=51;  % No. of grids in Y-axis
N=25;   % No of grids in the coil ( X-Y plane)
Ra=6;    % Radius of the coil in the X-Y plane
I=3;    % current in the coil
u0=1;   % for simplicity, u0 is taken as 1 (permitivity)
phi=-pi/2:2*pi/(N-1):3*pi/2; % For describing a circle (coil)

Xc=Ra*cos(phi); % X-coordinates of the coil
Yc=Ra*sin(phi); % Y-coordinates of the coil

yp(1:51)=-25:1:25; % Y-coordinates of the plane
zp(1:51)=0:1:50;% Z-coordinates of the plane

Y(1:Ny,1:Nz)=0; % This array is for 1-d to 2-d conversion of coordinates
Z(1:Ny,1:Nz)=0;

for i=1:Ny
    Y(i,:)=yp(i); % all y-coordinates value in 2-d form
end
for i=1:Nz
    Z(:,i)=zp(i);% all z-coordinates value in 2-d form
end

% calculate R-vector from the coil(X-Y plane)to Y-Z plane
%find the magnetic field and also the dl-vector along the coil current
% R is the position vector pointing from  (X-Y plane)coil to
%  the magnetic field in Y-Z plane


for a=1:Ny  %in for loop is along Y
for b=1:Nz  %is along Z-axis-

for i=1:N-1
Rx(i)=-0.5*(Xc(i)+Xc(i+1));
Ry(i)=(Y(a,b)-(0.5*(Yc(i)+Yc(i+1))));
Rz(i)=Z(a,b);
dlx(i)=Xc(i+1)-Xc(i);
dly(i)=Yc(i+1)-Yc(i);
end
Rx(N)=-0.5*(Xc(N)+Xc(1));
Ry(N)=(Y(a,b)-(0.5*(Yc(N)+Yc(1))));
Rz(N)=Z(a,b);
dlx(N)=-Xc(N)+Xc(1);
dly(N)=-Yc(N)+Yc(1);

%dl is the current element vector in the coil
%dl cross R is the curl of vector dl and R
%calculate dl cross R

for i=1:N
Xcross(i)=dly(i).*Rz(i);
Ycross(i)=-dlx(i).*Rz(i);
Zcross(i)=(dlx(i).*Ry(i))-(dly(i).*Rx(i));
R(i)=sqrt(Rx(i).^2+Ry(i).^2+Rz(i).^2);
end


% the biot savarts law equation

Bx1=(I*u0./(4*pi*(R.^3))).*Xcross;
By1=(I*u0./(4*pi*(R.^3))).*Ycross;
Bz1=(I*u0./(4*pi*(R.^3))).*Zcross;

% magnetic field from all current
BX(a,b)=0;       % Initialize sum magnetic field to be zero first
BY(a,b)=0;
BZ(a,b)=0;

for i=1:N   % loop over all current elements along coil
    BX(a,b)=BX(a,b)+Bx1(i);
    BY(a,b)=BY(a,b)+By1(i);
    BZ(a,b)=BZ(a,b)+Bz1(i);
end

end
end

figure(5)
plot(Xc,Yc,'linewidth',3)
axis([-20 20 -20 20])
xlabel('X-axis','fontsize',14)
ylabel('Y-axis','fontsize',14)
title('square loop co-ordinates','fontsize',14)
h=gca;
get(h,'FontSize')
set(h,'FontSize',14)
h = get(gca, 'ylabel');
fh = figure(5);
set(fh, 'color', 'white');
grid on

figure(6)
lim1=min(min(BZ));
lim2=max(max(BZ));
steps=(lim2-lim1)/100;
contour(zp,yp,BZ,lim1:steps:lim2)
axis([1 50 -25 25])
xlabel('Z-axis','fontsize',14)
ylabel('Y-axis','fontsize',14)
title('BZ component','fontsize',14)
colorbar('location','eastoutside','fontsize',14);
h=gca;
get(h,'FontSize')
set(h,'FontSize',14)
h = get(gca, 'ylabel');
fh = figure(6);
set(fh, 'color', 'white');


figure(7)
lim1=min(min(BY));
lim2=max(max(BY));
steps=(lim2-lim1)/100;
contour(zp,yp,BY,lim1:steps:lim2)
axis([1 50 -25 25])
xlabel('Z-axis','fontsize',14)
ylabel('Y-axis','fontsize',14)
title('BY component','fontsize',14)
colorbar('location','eastoutside','fontsize',14);
h=gca;
get(h,'FontSize')
set(h,'FontSize',14)
h = get(gca, 'ylabel');
fh = figure(7);
set(fh, 'color', 'white');


figure(8)
quiver(zp,yp,BZ,BY,2)
axis([1 50 -25 25])
xlabel('Z-axis','fontsize',14)
ylabel('Y-axis','fontsize',14)
title('B-field Vector flow','fontsize',14)
h=gca;
get(h,'FontSize')
set(h,'FontSize',14)
h = get(gca, 'ylabel');
fh = figure(8);
set(fh, 'color', 'white');

ans =

    10


ans =

    10


ans =

    10


ans =

    10


ans =

    10


ans =

    10

Published with MATLAB® R2015a