MATLAB calculations

%% First I define fixed constants

R=6.75e-2; % in m muo=4*pi*(1e-7); muB=9.274e-24; %using J h=6.626e-34; %using J N=320;

%% The data is then used to calculate the B-field through the Helmholtz %coils and the sample

%SMALL datS=[90.00 	1.839; 85.00 	1.766;     80.00 	1.685;      75.00 	1.567;      70.00 	1.477;]; fqS=(1e6)*datS(:,1)'; iS=datS(:,2)'; BS=((4/5)^(3/2))*((muo*N*iS)/R);

%MEDIUM datM=[70.00 	1.335 65.00 	1.253     60.00 	1.171      55.00 	1.071      50.00 	0.972      45.00 	0.898      40.00 	0.790      35.00 	0.690      30.00 	0.591      25.00 	0.492]; fqM=(1e6)*datM(:,1)'; iM=datM(:,2)'; BM=((4/5)^(3/2))*((muo*N*iM)/R);

%Large datL=[30.00 	0.581 26.00 	0.472     22.00 	0.427      18.00 	0.355      14.00 	0.265]; fqL=(1e6)*datL(:,1)'; iL=datL(:,2)'; BL=((4/5)^(3/2))*((muo*N*iL)/R);

%% Now I calculate g_s for each data pair and then from linear least square % fits for the 3 data sets

gSmall=(h*fqS)./(muB*BS) gSmean=mean(gSmall) gMed=(h*fqM)./(muB*BM) gMmean=mean(gMed) gLarge=(h*fqL)./(muB*BL) gLmean=mean(gLarge) gTot=(gSmean+gMmean+gLmean)/3

Sfit=polyfit(BS,(h*fqS)/muB,1) Sval=polyval(Sfit,BS) Mfit=polyfit(BM,(h*fqM)/muB,1) Mval=polyval(Mfit,BM) Lfit=polyfit(BL,(h*fqL)/muB,1) Lval=polyval(Lfit,BL) AvgFit=(Sfit(1)+Mfit(1)+Lfit(1))/3 figure(1) plot(BS,Sval,BS,(h*fqS)/muB,'r*');title('B vs.(h*v)/muB for small coil'),xlabel('T'),ylabel('T') saveas(figure(1),'smallcoil.jpg') figure(2) plot(BM,Mval,BM,(h*fqM)/muB,'r*');title('B vs.(h*v)/muB for medium coil'),xlabel('T'),ylabel('T') saveas(figure(2),'mediumcoil.jpg') figure(3) plot(BL,Lval,BL,(h*fqL)/muB,'r*');title('B vs.(h*v)/muB for large coil'),xlabel('T'),ylabel('T') saveas(figure(3),'largecoil.jpg')

sdmS=sqrt(sum((gSmall-gSmean).^2)*(1/(length(gSmall)*(length(gSmall)-1)))) sdmM=sqrt(sum((gMed-gMmean).^2)*(1/(length(gMed)*(length(gMed)-1)))) sdmL=sqrt(sum((gLarge-gLmean).^2)*(1/(length(gLarge)*(length(gLarge)-1)))) sdmTot=(sdmS+sdmM+sdmL)/3