# Electromotive force (voltage)

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Kutlu Yigitturk on 18 Jun 2021
This Matlab program below implements the two operations, print the eVec& eMag and animate the Faraday’s law for any specified v,B & l , &.
B = [0 0 1]'; v = [0 1 0]'; length = [1 1 1]'; length = length/norm(length);
eVec = cross(v,B); eMag = dot(eVec,length); az = 50; el = 15;
close all;
grn = [0 .8 0]; brn = [.8 .5 0];
Fig = figure; Fig.Position = Fig.Position + [-200 0 100 0];
subplot(1,2,1)
plot3([0 B(1)],[0 B(2)],[0 B(3)],'b','linewidth',3); hold on, grid on
plot3([0 v(1)],[0 v(2)],[0 v(3)],'color',grn,'linewidth',3);
plot3([0 eVec(1)],[0 eVec(2)],[0 eVec(3)],'r','linewidth',3);
text(B(1),B(2),B(3)*1.2,'B','color','b')
text(v(1),v(2)*1.2,v(3),'v','color',grn)
text(eVec(1)*1.0,eVec(2)-.2,eVec(3)+.2,'eVec','color','r')
text(-1.2,-1.5,-1,num2str(B),'color','b'), text(-1.2,-1.5,-.2,'B','color','b'),
text(-.5,-1.5,-1,num2str(v),'color',grn), text(-.5,-1.5,-.2,'v','color','b'),
text(0.2,-1.5,-1,num2str(eVec),'color','r'),text(0.2,-1.7,-.2,'eVec','color','r'),
text(0.9,-1.5,-1,num2str(length,4),'color',brn), text(0.9,-1.6,-.3,'Rod','color',brn)
title('eVec = cross(v,B) eMag = dot(eVec,length)')
set(gca,'color',[1 1 1]*.9)
axis('equal'), axis([-1 1 -1 1 -1 1]*1.5), view(az,el)
Rod0 = [-length length]*0.75; Rod = Rod0 + v*0;
plot3(Rod(1,:),Rod(2,:),Rod(3,:),'linewidth',6,'color',brn);
text(Rod(1,1),Rod(2,1),Rod(3,1)+.3,'Rod','color',brn)
text(Rod(1,2)-.4,Rod(2,2),Rod(3,2)-.3,['eMag = ',num2str(eMag)],'color',brn)
xlabel('x'), ylabel('y'), zlabel('z')
subplot(1,2,2)
plot3([0 B(1)],[0 B(2)],[0 B(3)],'b','linewidth',1); hold on, grid on
plot3([0 v(1)],[0 v(2)],[0 v(3)],'g','linewidth',1);
plot3([0 eVec(1)],[0 eVec(2)],[0 eVec(3)],'r','linewidth',1);
set(gca,'color',[1 1 1]*.9)
axis('equal'), axis([-1 1 -1 1 -1 1]*2),view(az,el)
xlabel('x'), ylabel('y'), zlabel('z')
BFldx = [0 0 -.02 .02 0 0 0 0]; BFldy = [0 0 0 0 0 -.02 .02 0]; BFldz = [-1 1 0.9 0.9 1 .9 .9 1]*1.5;
for i = -2:0.5:2
for j = -2:0.5:2
plot3(BFldx'+i,BFldy'+j,BFldz','linewidth',0.1,'color',[.5 .5 1]);
end
end
drawnow
DrawRod = plot3(Rod(1,:),Rod(2,:),Rod(3,:),'linewidth',6,'color',brn);
TexteMag = text(Rod(1,2)+.1,Rod(2,2)+.1,Rod(3,2)+.1,['+',num2str(eMag)],'color',brn);
Tit = title(['eVec^t = [',num2str([0 0 0]),'] eMag = ',num2str(0)]);
for n = 1:3
Rod = Rod0;
set(DrawRod,'xdata',Rod(1,:),'ydata',Rod(2,:),'zdata',Rod(3,:));
set(TexteMag,'pos',Rod(:,2)+.1,'string',num2str(0))
set(Tit,'string',['eVec^t = [',num2str([0 0 0]),'] eMag = ',num2str(0)]), pause(1)
for m = 0:0.02:1
eVec = cross(v,B); eMag = dot(eVec,length);
Rod = Rod0 + v*m;
set(DrawRod,'xdata',Rod(1,:),'ydata',Rod(2,:),'zdata',Rod(3,:));
set(TexteMag,'pos',Rod(:,2)+.1,'string',num2str(eMag))
set(Tit,'string',['eVec^t = [',num2str(eVec'),'] eMag = ',num2str(eMag)])
drawnow, pause(0.001)
end
end
At this point I don't know how to change the I matrix. How can I do that? Thank you for your help.

R2021a

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