Can anyone help, please?
Thanks!
Calculate the flux of the vector field F = (4-x)i through the cube with verticies (0,0,0),(5,0,0),(0,5,0),(0,0,5), oriented outwards.
First, I drew the cube. Since the vector field is only in the i direction, I eliminated all but two sides. Namely, the sides parallel to the x-axis. Is that a correct thing to do?
Secondly, I noted that the only sides that are perpendicular to the direction of the vector field at any point have the following attributes:
Surface #1: x = 0 at all points. Surface area = 25. This side is oriented towards -i.
Surface #2: x = 5 at all points, surface area also 25. This side is oriented towards +i.
Thus I figured it would be a simple problem of adding the fluxes through these two surfaces.
Surface #1:
Since x = 0 at all points, vector field F = 4i at all points on the surface. Since the orientation is -i, A vector = -25i.
Dotting these two vectors is just -100.
Surface #2:
Since x = 5 at all points, vector field F = -i at all points on the surface. Since the orientation is +i, Area vector = 25i.
Dotting these two vectors is -25.
And,
-100 + -25 = -125
So, what part of this is incorrect thinking? Care to shed some light?
Thank you!!