Find the flux of through where N is the upward unit normal vector to S.
A) 2
B) 3
C) 10
E) 5

Question

Find the flux of  through  where N is the upward unit normal vector to S.
A) 2 
B) 3 
C) 10 
E) 5

Quizplus · Accepted Answer

The flux of a vector field through a surface is given by the surface integral of the dot product of the vector field and the unit normal vector to the surface. In this case, the vector field is given by the scalar function 11eaa595_61fe_0965_a696_63033eee2ae6_TB4584_11_TB4584_11, which means that it has a constant value at every point. Therefore, the flux through the surface is proportional to the area of the surface oriented in the direction of the normal vector, which is upward. Since the surfaces have the same area, the flux is proportional to the difference in height between them, which is 3077 - 966 = 2111. Therefore, the flux is equal to 2111 times the constant value of the vector field, which is 11eaa595_61fe_0965_a696_63033eee2ae6_TB4584_11_TB4584_11 times 2111 = 11eaa595_61fe_3077_a696_158a08584cb5_TB4584_11_TB4584_11.

Find the Flux of Through Where N Is