Finding the Curl at a point with three squares

[pradeepk]

Homework Statement

Three small squares, S1, S2, and S3, each with side 0.1 and centered at the point (4,5,7), like parallel to the xy, yz, and xz planes respectively. The squares are oriented counterclockwise when viewed from the positive z, x, y axes respectively. A vector field G has circulation and S1 of -0.02, around S2 of 6, and around S3 of -5. Estimate Curl G at the point (4,5,7).

Homework Equations

Curl G ^. n=circulation density of G

The Attempt at a Solution

So they want the Curl of G, and the circulation is given.
So if I start with S1: CurlG ^. n= (-0.02)/(0.1)²

The thing I don't know how to find is the normal vector. I know that S1 is parallel to the xy plane so the normal vector wil be pointing up in the positive z direction.

Am I going about this problem correctly? Thank you

 

[lanedance]

if i read the question correctly, you have in effect a measurement of the projection of the curl in 3 orthogonal directions. What total curl vector would give you those projections?

 

[lanedance]

also for each given "square" the normal direction will eb normal to the plane, eg. for the xy plane, the normal direction is the z direction - you will have to check your conventions to find whether it is -ve or -ve z direction, i can't remember which...