How to use spherical Hankel fumction to obtain sphere scatter

c=3e8;
f=6e9;
n=10;
i=1:n;
Wl=c/f;
k=(2*pi)/Wl;
radius=1e-2:1e-4:6e-2;
r=length(radius);
kr=k*radius;
X=radius/Wl;
Ae=zeros(1,r);
syms nu x
J=sqrt(pi/(2*x)).*besselj(nu+0.5,x);
Y=sqrt(pi./(2*x)).*bessely(nu+0.5,x);
H=J-1j*Y;
dH=diff(H);
ht=H.*dH;
nu=i;x=kr;
B=eval(ht);

Error using besselj
NU and Z must be the same size or one must be a scalar.

Error in sym/eval (line 13)
s = evalin('caller',vectorize(char(x)));

    A(i,:)=(abs(((-1^i)*(2*i+1))./(B)).^2)./(4*pi);
    Ae(1,:)=A(i,:)+Ae(1,:);

figure(1);
plot(X,Ae);

we want to use this formula to evaluate the echo area of a conducting sphere of radius a，the upper code is my try，but it didnt work. Please someone tell me what's wrong with my code，thank you.

Answer 1

[Aakash]

The error in your code arises from the fact that the variable nu is a symbolic variable defined using syms, while x is a numeric array (kr). The besselj function requires both inputs to have the same size or one to be a scalar.

To fix this, you can use a for loop to evaluate the expression for each value of i and radius like this:

c = 3e8;

f = 6e9;

n = 10;

i = 1:n;

Wl = c / f;

k = (2 * pi) / Wl;

radius = 1e-2:1e-4:6e-2;

r = length(radius);

kr = k * radius;

X = radius / Wl;

Ae = zeros(1, r);

for i = 1:n

B = zeros(1, r);

for j = 1:r

x = kr(j);

H = besselj(i, x) - 1j * bessely(i, x);

dH = (1/2) * (besselj(i-1, x) - besselj(i+1, x) - 1j * (bessely(i-1, x) - bessely(i+1, x)));

ht = H * dH

B(j) = subs(ht, x, kr(j))

end

A = (abs(((-1)^i) * (2 * i + 1) ./ B).^2) / (4 * pi);

Ae = A + Ae;

end

figure(1);

plot(X, Ae);

[Dyuman Joshi]

There's no point of using subs(), as there is no symbolic expression or function in the code.

Also, you can define H and dH as function handles, and calling them for each iteration and directly substituting input values.

Another good practice is to not use i and j as loop indices, especially when you will be using any or both of them as the imaginary constant.