MediumCalculusca-158

Stokes Circulation Numeric

Problem

Compute the counterclockwise circulation of F = [-c*y, c*x] around the boundary of the unit square [0, 1]^2.

Parameterize each edge and apply the midpoint rule with n segments per edge. Since the field is linear the midpoint rule is exact and the circulation equals 2c, matching the curl integral.

Hint

Only the right and top edges contribute; the field is tangent to the bottom edge and zero along the left one.

Test cases

case 1

in: [1,4]

expected: 2

case 2

in: [-2,10]

expected: -4

case 3

in: [0,5]

expected: 0

case 4

in: [3,1]

expected: 6

Starter codePython

def stokes_circulation(c, n):
    # Your code here
    pass

4 test cases · run your code against them in the editor