I want to know how to solve Green's Theoreom

i have Bn and Bt data sheet and u0=4*pi*10^(-7)

this is inclosed curve integral how can i solve this integral in matlab?

plz help

[Roshan Swain]

Try using "integral" : Numerical integration - MATLAB integral (mathworks.com)

You can also take a look at : Complex Line Integrals - MATLAB & Simulink (mathworks.com)

Answer 1

[William Rose]

@명우,

The advice from @Roshan Swain is very good.

Share your table of Bn, Bt, and share the path you plan to take. (The path is represented by lower case L in your equation, and should be counter-clockwise.)

The formula in the image you shared does not look like a standard presentation of Green's theorem.

A standard representation of Green's theorem is

(1)

where dl is a small element along the path C, and F is a vector field.

F can be written as

(2)

In this case, the left hand side of the equation 1 above can be rewritten as follows:

(3)

In the equation you provided, the dot, representing dot product, is missing, and the quantity corresponding the the vector field F of equation 1 above is

but this looks like a scalar, not a vector. What are the x- and y- components of F, or the n- and t- components? You will need these components in order to compute the numerical version of the dot product of F with the path element, dl.