Find the flux of the field Fxiyjzk across the portion of the

Find the flux of the field F=xi+yj+zk across the portion of the sphere x^2+y^2+z^2=a^2 in the first octant in the direction away from the origin.

Solution

flux=? dA (F.n)dA F is the vector field n is the unit normal to the surface. F · n = [x,y,z] · [x/a,y/a,z/a] = (x²+y²+z²)/a = a²/a = a The integral that remains is just the area of the surface= 1/6 pa³ Flux= 1/6 pa4.