1. The problem statement, all variables and given/known data (The S1 after the double integral is supposed to be underneath them btw, I just can't seem to do it right using LaTeX right now so bear with me please.) Suppose F is a radial force field, S1 is a sphere of radius 9 centered at the origin, and the flux integral ∫∫S1F⋅dS=4. Let S2 be a sphere of radius 81 centered at the origin, and consider the flux integral ∫∫S2F⋅dS. (A) If the magnitude of F is inversely proportional to the square of the distance from the origin,what is the value of ∫∫S2F⋅dS? (B) If the magnitude of F is inversely proportional to the cube of the distance from the origin, what is the value of ∫∫S2F⋅dS? 2. The attempt at a solution So the flux integral over S1 has a value of 4. The Flux integral can be evaluated by multiplying the magnitude of F times the surface area of the sphere: 4pi r^2. Solving for the magnitude of F I get that it's (1/pi r^2). For part A, I just used this magnitude because it matches the fact that it has to be inversely proportional to the square of the distance from the radius. And so I got the right answer which is 4. For part B however just increasing the proportionality to be (1/pi r^3) doesn't work, so I don't know what I'm missing here. I'd like to know first, how we know that the flux integral is equal to the magnitude of F times the surface area of whatever given surface there is. I was just told this, and I can't find it on the textbook, so I'd like to first understand what is the methodology used behind solving this problem. Thank you. Also, does anyone know of a resource similar to Paul's Online Math Notes that would cover Surface Integral more thoroughly?