in this problem, we are asked to prove divergence and curl theorem
So we break our problem into sub problems taking each side of eqaul signand then simplifying it.
2.1 2.2 2 FUNDAMENTAL THEOREMS Consider the vector function u x2+ yj)+12. 2.1 15 POINTS Verify...
1 For a vector field A zx +xz y yz Verify Divergence theorem over a sphere, with a radius R and center at the origin 1. 3 points 3 points Converthe vector into eylindrical coordinatces 2. 1 For a vector field A zx +xz y yz Verify Divergence theorem over a sphere, with a radius R and center at the origin 1. 3 points 3 points Converthe vector into eylindrical coordinatces 2.
2.1 2.2 2.3 2 BALL AND PLANE Consider a spherical shell of radius R and charge per unit area ơi sitting at the origin. There is also an infinite plane parallel to the x - y plane sitting at zzo with charge per unit area σ2. We will take z02R. Compute the electric field at the following locations: 2.1 10 POINTS The origin. 2.2 15 POINTS The point (xo.0,0) with xo>R 2.3 15 POINTS The point (x1,0, z) with 0...
3) (11 points) Consider the vector field Use the Fundamental Theorem of lLine Integrals to find the work done by F along any curve from 41. 1Le) to B(2. el) 4) (10 points) Consider the vector field F(x.y)-(r-yi+r+y)j and the circle C: r y-9. Verify Green's Theorem by calculating the outward flux of F across C (12 points) Find the absolute extreme values of the function .-2-4--3 on the closed triangular region in the xy-plane bounded by the lines x...
NO.25 in 16.7 and NO.12 in 16.9 please. For the vector fied than the vecto and outgoing arrows. Her can use the formula for F to confirm t n rigtppors that the veciors that end near P, are shorter rs that start near p, İhus the net aow is outward near Pi, so div F(P) > 0 Pi is a source. Near Pa, on the other hand, the incoming arrows are longer than the e the net flow is inward,...