Final answer:
To calculate the net outward flux for the vector function A=10R through the surface of a sphere with radius 0.8, one would use the area of the sphere to determine the total flux, resulting in a straightforward multiplication since the vector function is spherically symmetric.
Step-by-step explanation:
The question asks for the calculation of the net outward flux of a vector function A = 10R (in spherical coordinates) through the surface of a sphere of radius 0.8 centered at the origin. In spherical coordinates, the vector A has only the radial component and its magnitude is proportional to the scalar function 10R. Since the vector A is purely radial, the flux through a spherical surface will only depend on the area of the sphere and the magnitude of A.
To calculate the electric flux, we can use Gauss's law which states that the electric flux through a closed surface is equal to the charge enclosed divided by the permittivity of free space (ε0). However, we are not given any charge, rather a vector function. We proceed by integrating the field over the surface of the sphere. The area of the sphere is A = 4π(0.8)2, and the magnitude of vector A is constant over the surface for a fixed radius. The net flux Φ through the surface is then Φ = A ⋅ A = (4π(0.8)2) ⋅ (10 ⋅ 0.8) = 4π(0.8)3 ⋅ 10.