Question

calculate the flux of the vector field vector f = 3vector i 6vector j through a square of side 4 lying in the plane x y z = 10 oriented away from the origin.

Answer 1

To calculate the flux of the vector field F = 3i + 6j through a square of side 4 lying in the plane xyz = 10, oriented away from the origin, we can use the formula Flux = ∬S F · dS.

Step-by-step explanation:

To calculate the flux of the vector field F = 3i + 6j through a square of side 4 lying in the plane xyz = 10, oriented away from the origin, we need to find the surface integral of the dot product between the vector field and the unit normal vector to the surface. The flux can be calculated using the formula:

Flux = ∬S F · dS

Since the square lies in the plane xyz = 10, the unit normal vector to the surface is given by n = (0, 0, 1). Substituting the values into the formula, we have:

Flux = ∫∫S (3i + 6j) · (0, 0, 1) dS

As the square has side 4, its area is 16. Therefore, the flux is:

Flux = (3i + 6j) · (0, 0, 1) × 16