Calculate the flux of the field F across the closed plane curve C.
-F = (x+y)i + xyj; the curve C is the closed counterclockwise path around the rectangle with vertices at (0, 0), (3, 0), (3, 10), and (0, 10)
A) 175
B) 85
C) 120
D) 75

Question

Quizplus · Accepted Answer

Applying the divergence theorem, we have
∬S F · dS = ∭V (∂Fx/∂x + ∂Fy/∂y)dV
where S is the closed surface that encloses the volume V.
Using ∂Fx/∂x + ∂Fy/∂y = 1 + x, we have
∭V (∂Fx/∂x + ∂Fy/∂y)dV = ∫0³ ∫0¹⁰ ∫0^(1+x) (1 + x) dz dy dx = 75
Therefore, the answer is D.

Calculate the Flux of the Field F Across the Closed