Consider the vector field .
Find the flux of the given vector field through a cube in the first octant with edge length c, one corner at the origin and edges along the axes.
I need to find the flux at each sides of the cube, can someone help me how I can do this?
Use the divergence thm --beats 6 flux integrals
Flux = volume integral( divF) in this case divF =1
so you have simply c^3 for the flux
If you absolutely have to do 6 Flux calculations
since the x and z components are constant the flux through the bottom
cancels the flux through the top. Similarly for the front and back since the x component is 0
On the left side y= 0 so the flux is 0
the right face then is the only contribution to the flux
where y =c and you integrate over the square with sides c in the xzplane
The definiton of Flux is
Since each of the sides of the cube are parallel to a coordinate axisis the normal vectors will be the unit vectors i, j k.
I will set one up for you
So on the top of the cube the normal vector point up in the Z direction.
You will need to do this with the other 5 sides and then add all of them up.