Estimate Vector Field Surface Integral

[maxhersch]

I assume this is a simple summation of the normal components of the vector fields at the given points multiplied by dA which in this case would be 1/4.

This is not being accepted as the correct answer. Not sure where I am going wrong. My textbook doesn't discuss estimating surface integrals of vector fields but I assume it's done this way, similar to any other integral. Any help would be greatly appreciated. Thanks.

 

[slider142]

Hi maxhersch,

The vector <1/4, 3/4, 1> is not a unit normal vector pointing in the positive z direction. It is a vector that points along the direction between the origin and the point (1/4, 3/4, 1). A unit normal vector pointing in the positive z-direction is <0, 0, 1>. The point that this vector is attached to for the purpose of carrying out this integral is (1/4, 3/4, 0), but in the usual formalism of Gibbs vector calculus, we do not usually show this second condition.
Recall that each point is assigned its own unit normal vector for the purpose of carrying out the integral, but the coordinates of the point do not appear as components of the unit normal vector. They are relatively indepedent numbers, as the direction of the unit normal vector is determined by the orientation of a small section of surface containing the point, not the point all by itself.

 

[maxhersch]

Hi maxhersch,

The vector <1/4, 3/4, 1> is not a unit normal vector pointing in the positive z direction. It is a vector that points along the direction between the origin and the point (1/4, 3/4, 1). A unit normal vector pointing in the positive z-direction is <0, 0, 1>. The point that this vector is attached to for the purpose of carrying out this integral is (1/4, 3/4, 0), but in the usual formalism of Gibbs vector calculus, we do not usually show this second condition.
Recall that each point is assigned its own unit normal vector for the purpose of carrying out the integral, but the coordinates of the point do not appear as components of the unit normal vector. They are relatively indepedent numbers, as the direction of the unit normal vector is determined by the orientation of a small section of surface containing the point, not the point all by itself.

Perfect thanks a lot