# Green's Theorem : Flux

Let C be a differentiable curve contained in the portion 0 inferior or equal to x inferior or equal to 1 of the first quadrant, starting on the positive y-axis and ending somewhere on the line x=1.

Show that the flux of the vector field F

F=(2xy-2x^4*y)i+(4x+4x^3y^2-y^2)j

across C is always equal to -2.

Hint : Apply Green Theorem to the region between C and the x-axis.

Â© BrainMass Inc. brainmass.com March 4, 2021, 6:04 pm ad1c9bdddfhttps://brainmass.com/physics/flux-flux-density/greens-theorem-flux-27353

#### Solution Summary

Flux is investigated using Gren's theorem. The solution is detailed and well presented.

$2.49