Is it possible to vary 5 variables in an equation using linspace and plot 3 of them using contour?

I have an equation of a physical system and I want to vary 5 parameters (i, N, r1, r2 and L) using linspace or :. My aim to find that an optimum configuration (i.e. a set of values of these variables) that gives me the maximum value of field. However, I get an empty plot when I run this code and I also get an error saying "Undefined function or variable 'field'."

Moreover, I get the values of t =r2-r1 as zero for all values in the workspace.

I would really appreacite if someone could kindly help me.

Thank you in advance.

uo = 1.26*(10^-3);
L=linspace(1,70);
N=linspace(100,1000,10);
i=linspace(1,5,10);
r1=linspace(1,50,100);
r2=linspace(1,50,100);
x1= 10;
x2= x1+L;
t=r2-r1;
[L,t] = meshgrid(L,t);
if r2>r1
g=sqrt((r2.^2)+(x2.^2));
m=sqrt((r1.^2)+(x2.^2));
n=sqrt((r2.^2)+(x1.^2));
o=sqrt((r1.^2)+(x1.^2));
A = reallog((g+r2)./(m+r1));
B = reallog((n+r2)./(o+r1));
field = ((uo.*N.*i)./(2.*L*(r2-r1))).*((x2.*A)-(x1.*B));
end
figure
contour(L,t,field)

[Walter Roberson]

field is not defined unless r2>r1 . However,

r1=linspace(1,50,100);
r2=linspace(1,50,100);

so they are both vectors of the same size and same content, so r2 > r1 is never true because r2 == r1

Answer 1

[Walter Roberson]

uo = 1.26*(10^-3);

Lvec = linspace(1,70);
Nvec = linspace(100,1000,10);
ivec = linspace(1,5,10);
r1vec = linspace(1,50,100);
r2vec = linspace(1,50,100);

[L, N, i, r1, r2] = ndgrid(Lvec, NVec, ivec, r1vec, r2vec);

x1= 10;
x2= x1+L;
t=r2-r1;

Z = zeros(size(r2));
field = Z;

mask = r2 > r1;

g = sqrt((r2(mask).^2)+(x2(mask).^2));
m = sqrt((r1(mask).^2)+(x2(mask).^2));
n = sqrt((r2(mask).^2)+(x1(mask).^2));
o = sqrt((r1(mask).^2)+(x1(mask).^2));
A = reallog((g+r2(mask))./(m+r1(mask)));
B = reallog((n+r2(mask)./(o+r1(mask))));
field = ((uo.*N(mask).*i(mask))./(2.*L(mask)*(r2(mask)-r1(mask)))).*((x2(mask).*A)-(x1(mask).*B));

[maxfield, maxixd] = max(field);
LNir1r2 = [L(maxid), N(maxid), i(maxid), r1(maxid), r1(maxid)];   %parameter values at maximum

However, do not try to contour field: it is a 5 dimensional variable. You can do things like a "maximum projection" over a 2D subset of the values:

p134 = squeeze(max(field, [], [1 3 4]));
contour(Nvec, r2vec.', p134);