Using green's theorem, find the counterclockwise circulation and

ASHWIN KRISHNA

ASHWIN KRISHNA

Answered question

2022-05-22

Using green's theorem, find the counterclockwise circulation and outward flux for field F and curve C, if:

 

i) F=(x²+4y)i+(x+y²)j, C:The Square bounded by x=0,x=1,y=0,y=1

 

 

Answer & Explanation

Jeffrey Jordon

Jeffrey Jordon

Expert2022-11-08Added 2605 answers

We have given F=(x2+4y)i+(x+y2)j C: the square bounded by x=0,x=1,y=0,y=1 in the xy-plane

we have given R=(x,y):0x1,0y1

Let P=(x2+4y),Q=(x+y2)

by using Green's Theorem dP/dy=4,dQ/dx=1

Circulation =integration of F.dr over C

=integration of (dQ/dx-dP/dy)dA over R

=integration of (x=0 to 1) integration of (y=0 to 1) (1-4)dydx

=integration of (x=0 to 1) integration of (y=0 to 1) (-3)dydx

=integration of (x=0 to 1)(-3y) (y=0 to 1) dx

=integration of (x=0 to 1)(-3)dx

=(-3x) from x=0 to 1

Circulation =-3

the circulation for the field F around the curve C is -3

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?